Christian Bidard

GETTING RID OF RENT?

Keywords: Land, Rent, Ricardo, Sra¤a, Trade-o¤ JEL classi…cations: B12, B51, D24, D33

In order to extend the theory of value and the trade-o¤ property to economic systems with lands, Ricardo reduced their study to that of productive systems without lands by considering the marginal agricultural methods. Sra¤a generalised the analysis to prices of production and rejected the notion of order of cultivation. The strategy works sometimes for extensive cultivation, fails in most cases of intensive cultivation, and always when the net product of agriculture is increased by making use of corn saving methods in industry.

Introduction

In the last quarter of the twentieth century, the rise in the price of oil exerted long-term e¤ects on productive systems. Two main types of adaptation can be distinguished. First, the higher price provided an incentive to produce more oil, because it made some costly …elds pro…table and led to the use of more productive methods on the existing …elds and to the research of new …elds. Second, oil saving methods have been operated. The classical theory of rent, as set out by Ricardo (Essay, 1815; Principles, 1817) and developed by his successors, proposes intellectual tools to understand these evolutions. The …rst e¤ects concern the oil industry itself, and the phenomena at stake Address for correspondence: University Paris Ouest, EconomiX, Department of Economics, 200 avenue de la République, 92001 Nanterre, France; e-mail: christian.bidard@u-paris10.fr y Seminar at Centro Sra¤a (Roma), in collaboration with Dipartimento di Economia, Roma Tre University, 11 April 2013. 1 are related to the theory of either extensive or intensive rent. The study of the second e¤ect is less clear: does the substitution lead to the immediate replacement of a method by another, as in the case of industrial processes when distribution changes, or to the coexistence of two methods, one being more expensive and more productive than the other, as explained by Sra¤a (PCMC, 1960) for the intensi…cation of cultivation? In any case, Ricardo was less interested in the distinction between the types of rent than in their theoretical unity, the unifying principle being that 'the capital last employed pays no rent' (Principles, Chapter 2). As a consequence, he argued, the labour theory of value still holds in the presence of lands (given our theoretical purpose, we will refer to agricultural products and lands rather than oil and oil …elds), provided that one takes into account the marginal methods of production in agriculture. Translated in terms of the contemporary approach developed by Sra¤a, who formalised the theory of prices of production and studied their properties, productive systems with lands behave like singleproduct systems. For Ricardo, their most important property is the trade-o¤ between wages and the rate of pro…ts. In the presence of lands, the property is enriched by an additional trade-o¤ between rents and pro…ts which justi…es his plea for free trade.

In this paper, we review the di¤erent types of rent and reexamine the validity of Ricardo's theoretical strategy, with a speci…c attention to two connected questions: is an economic system with land reducible to a system without land? does the trade-o¤ property hold? Since our aim is to examine whether the analytical framework can be extended to the presence of lands, we do not discuss the labour theory of value itself and the same question applies to Sra¤a's formalisation. Sra¤a's critique of the notion of order of cultivation is deemed to lead to a greater generality without altering the attached economic properties. Section 2 reminds us the main features of Ricardo's analysis of rent and their applications to the theory of extensive cultivation, which are more restrictive than expected. Section 3 on intensive rent explains the di¤erences between Ricardo's and Sra¤a's conceptions and shows that the adoption of Sra¤a's enlarged framework is made at the expense of a signi…cant weakening in the properties of the economic system. Finally, Section 4 shows some dramatic consequences of the existence of a third type of rent for both Ricardo's and Sra¤a's approaches.

Some features of Ricardo' s approach

The main potential objection to the labour theory of value does not concern 'some rare statues and pictures'(Principles, Chapter 1) but the use of land in production, since land itself is not produced. Ricardo considered two possibilities, the extension and the intensi…cation of cultivation, to overcome the scarcity of corn. The …rst process consists in extending production to another land and sustains the ideal type of rent: the marginal land, which is the least productive in use, pays no rent. By contrast, the intensi…cation process consists in improving productivity on the same land. Have both processes the same economic properties? For Ricardo, their theoretical unity is rooted in the principle that the marginal capital pays no rent. Ricardo's analytical strategy is clearly explained in his letter to Mac Culloch dated 13 June 1820: 'By getting rid of rent, which we may do on the corn produced with the capital last employed, and on all commodities produced by labour in manufactures, the distribution between capitalist and labourer becomes a much more simple consideration'(Works, VIII, p. 194). Long-term prices are equal to the labour values determined by the industrial methods and the marginal agricultural methods. These values once obtained, the levels of the rents o¤set the cost di¤erences between the marginal method and the others: prices are determined …rst, then rents. The formal two-step procedure re ‡ects a logical hierarchy: '[T]he high price of corn [is] the cause of rent' (Principles, Chapter 2).

Ricardo's approach is dynamic. With the development of capitalism, more and more workers are employed and the net product of corn must increase. As long as the activity levels of the presently operated agricultural methods can be adapted to the evolution of demand, the prices and rents do not change. A limit is reached when some land becomes fully cultivated. Then the price of corn rises su¢ ciently to allow for the introduction of a new method, and that higher price sustains the payment of a rent on the previous marginal land. Prices and rents rise spasmodically whereas, on the physical side, one method of production is introduced at a low activity level and is progressively extended.

The notion of an order of cultivation is in line with the dynamic approach. Ricardo presumed that production on some quality of land would require more of each capital good than another ('Supposing then the land to be equally fertile, the necessity of employing more labourers, horses, &c. to carry the produce from the place where it was grown, to the place where it was to be consumed [...] would make it necessary that more capital should be permanently employed to obtain the same produce', Essay, p. 13); or: '[B]ecause more workers would be employed on the more distant or less fertile land, in order to obtain the same supply of raw produce', Essay, p. 18), so that the order of cultivation follows the ranking of lands according to intrinsic qualities. However, that answer does not su¢ ce to determine the choice between an extension of cultivation on a land of lower quality and its intensi…cation on the same land, and Ricardo gave some hints on a more general criterion: a given amount of capital is invested in the place where it yields a maximum physical product of corn. In the Essay, calculations are made in terms of corn. An equivalent form of the criterion makes reference to prices, as in the note attached to the end of Chapter 2 of the Principles (the same numerical example is used later): Ricardo calculated the successive prices of corn associated with the successive marginal lands, and the order of cultivation coincides with the order of prices. The quantity criterion (maximum product) and the price criterion (minimum rise) are dual. In modern terms, the sequence of prices and rents follows from the law of the one and minimum price induced by competition between farmers.

In Chapter IX of PCMC, entitled 'Land', Sra¤a adopted Ricardo's dynamical approach in that he studied how the economic system adapts itself to the evolution of the net product: 'The existence side by side of two methods can be regarded as a phase in the course of a progressive increase of production on the land'(PCMC, Section 88). This statement is all the more noteworthy that it contradicts the explicit warning of the Preface ('No changes in output [...] are considered'). Sra¤a introduced a systematic distinction between capital as an amount of money and capital as a set of capital goods and adopted cost-minimisation as criterion for the choice of methods. Chapter IX is therefore intimately linked with Chapter XII, entitled 'Switch in methods of production'. The universality of the cost-minimisation criterion makes Ricardo's a priori ranking of the lands useless and can even serve to criticise that idea: as relative costs depend on prices and therefore on distribution, a cheaper agricultural method at some rate of pro…ts may become more expensive at another rate and, then, the order of cultivation varies with distribution.

The study of extensive cultivation proper illustrates those general principles. To avoid any interference with intensive cultivation, we assume that each type of land is specialised in the production of a unique agricultural good and sustains a unique method of production. The prices are determined by the industrial methods and the marginal agricultural methods for the agricultural goods. As these methods constitute a productive system of the single-product type, one can conclude to the trade-o¤ between wages and pro…ts. Moreover, since rents increase spasmodically at the expense of profits, there is also a trade-o¤ between rents and pro…ts: 'In the course of these observations, I have often had occasion to insist, that rent never falls without the pro…ts of stock rising'(Essay, p. 38); therefore, 'the interest of the landlord is always opposed to the interest of every other class in the community' (Essay, p. 21), a basic statement for Ricardo's recommendations on economic policy. Ricardo's assertions on land and rent seem fully justi…ed. However, the reader's attention must be drawn on the following point. In spite of common wisdom that extensive cultivation is well understood and constitutes a model for further studies on rent, the trade-o¤ property has only been proved in a restrictive framework. Compare the following two statements:

-In a multisector model without land, there is a trade-o¤ between wages and pro…ts. The cost-minimising methods are indeed those which appear on the upper envelope of all r-w curves and, each curve being decreasing, the same for their envelope whatever the number of methods in each branch.

-In a multisector model with lands and extensive cultivation proper, the property holds if there is only one agricultural good and if the industrial methods are given (one method per industrial branch).

Since a marginal agricultural method pays no rent and can be identi…ed with an industrial method, the reason why the …rst statement cannot be transposed to several agricultural goods and several methods in each industrial branch is unclear at this stage. We shall return in Section 4 to the reason of this unfortunate restriction (we should have written above that 'the prices are determined by the given industrial methods and the unique marginal method for corn').

Intensive rent and trade-o¤

In the Principles, Ricardo introduced the notion of intensive cultivation by the sentence: 'It often, and, indeed, commonly happens, that before No. 2, 3, 4, or 5, or the inferior lands are cultivated, capital can be employed more productively on those lands which are already in cultivation' (Chapter 2). To isolate intensive cultivation proper, let us assume that land is uniform in quality. Again, Ricardo assumed that the intensi…cation process consists in depositing an additional layer of capital and labour over a pre-existing process. Sra¤a made no hypothesis of that type and, for him, a more intensive process is 'more expensive and more productive'per acre. Intensive rent stems from the coexistence of two methods on a fully cultivated land: as the costs of production for capital and labour are lower for process A but process B is more productive, there exists a unique positive level of the rent per acre which uniformises the price of corn produced by both methods.

A reference to a corn model with land illustrates the gap between Ricardo's and Sra¤a's conceptions and su¢ ces to understand the points at stake in the theory of intensive rent. Let corn be produced by means of corn and labour on a homogenous and fully cultivated land. Following Sra¤a, intensive cultivation is characterised by the coexistence of two agricultural methods, which we write as (method A) a 1 qr. corn + l 1 labour + 1 acre land ! 100 qr. corn (method B) a 2 qr. corn + l 2 labour + 1 acre land ! 185 qr. corn By assumption, method B is more productive than A in terms of net product par acre (185 a 2 > 100 a 1 ) and the distribution variables are such that B is more expensive than A. The net product of corn is increased by extending the area cultivated by method B at the expense of method A. Ricardo's restrictive hypothesis is that the magnitudes a = a 2 a 1 and l = l 2 l 1 are both positive. Ricardo assumed that method A is …rst used on the totality of the soil, while the second process consists in spreading an additional layer of capital and labour on a part of the soil. In other words, in Ricardo's conception, the original data are represented by method A and another method written as (method ) a qr. corn + l labour ( + 1 acre land) ! 85 qr. corn with the restriction that method can only be used after method A. The production of corn is increased by extending the additional coat of capital and labour over the pre-existing method. As the rent per acre is entirely paid by the initial method (farmers do no pay the rent twice), the A-model justi…es Ricardo's claim that the marginal capital pays no rent. 1Let us look at the determination of prices and rents and the trade-o¤ property. In Ricardo's approach, the value of corn is entirely de…ned by the marginal conditions of production, i.e. by method . Land is ignored as that method pays no rent. The value of corn once known, method A determines the rent per acre: the parallel with extensive rent is perfect. In Sra¤a's approach, the price p (with labour as numéraire) and the rent per acre are the solution to two equations:

(1 + r)a 1 p + l 1 + = 100p (1) (1 + r)a 2 p + l 2 + = 185p (2)
Rent disappears by subtraction, and equation ( 3)

(1 + r)( a)p + l = 85p (3)
determines the price of corn …rst. In a second step, the level of rent is found by returning to any of the original equations. The assumptions retained ensure that the price and the rent are both positive. The formal similarity between Ricardo's and Sra¤a's approaches hides deep di¤erences in the interpretation and the properties of the model: if either a or l is negative, as admitted by Sra¤a, the price equation ( 3) is not sustained by a physical method. As a consequence, for a zero rate of pro…ts, the price of corn cannot be interpreted in terms of labour values. And, for positive rates of pro…ts, the trade-o¤ property between wages and pro…ts cannot be presumed. To study that point, let us rewrite equation [START_REF] Bidard | Prices, Reproduction, Scarcity[END_REF] with corn as numéraire. The transformed equation

(1 + r)( a) + w l = 85 (4)
shows that the real wage w and the rate of pro…ts r move in opposite directions when a and l are positive (Ricardo), in the same direction if one of them is negative (Sra¤a)! These conclusions extend to general multisector models: except in special cases, a productive system à la Sra¤a with homogenous land cannot be reduced to a single-product system without lands. At an abstract level, the origin of the di¢ culty lies in the presence of negative multipliers in the standard system, as one must subtract the inputs of method A from those of method B to eliminate land from the input side (PCMC, section 87). But Sra¤a did not draw the economic implications of that lacuna and his conclusions are over-optimistic.

The economic consequences of external rent

When demand evolves exogenously and corn becomes scarce, there are three and only three logical possibilities to overcome that limit by introducing a new method of production: either it is a new corn method on another land, or a new corn method on the same land, or it is not a corn method. The …rst possibility leads to the notion of extensive rent, the second to that of intensive rent, the third to that of external rent. In post-Sra¢ an economics, after Quadrio-Curzio's (1967) and [START_REF] Montani | La teoria ricardania della rendita[END_REF][START_REF] Montani | Scarce natural resources and income distribution[END_REF]) initial studies, the …rst two notions have inspired dozens of papers and books (see e.g. [START_REF] Abraham-Frois | Rentes, rareté, surpro…ts[END_REF]Bidard, 1987;Steedman, 1988;[START_REF] Kurz | Theory of Production[END_REF][START_REF] Bidard | Prices, Reproduction, Scarcity[END_REF]. By contrast, the notion of external rent is hardly mentioned in the economic literature and, when it is the case, it is only set out as a curiosity. It was introduced by [START_REF] Saucier | Le choix des techniques en situation de limitation de ressources[END_REF] in his PhD thesis as 'external di¤erential rent'. External rent has some similarity with intensive rent, but its working relies on the interdependencies between industries and a substitution e¤ect.

When corn is scarce, its price rises until a new method becomes pro…table. In the Essay (p. 35), Ricardo claimed that only the price of corn changes, but he modi…ed his opinion later: as corn enters into the production of the other commodities, their prices also increase, though in lesser proportions. These compensating variations are not mentioned in Chapter 2 of the Principles but are explicit in those devoted to taxation ('The probable e¤ect of a tax on raw produce, would be to raise the price of raw produce, and of all commodities in which raw produce entered, but not in any degree proportioned to the tax', Chapter 9). For simplicity, let us retain Sra¤a's assumption of a given rate of pro…ts and consider a basic bisector model with, at the initial stage, one method producing corn and another iron (call it method C). Following an increase in the demand for corn and a rise in its price, the price of iron is adjusted in order to maintain the pro…tability of method C. The initial rise improves the pro…tability of all corn methods; the compensating rise for iron improves the pro…tability of those iron methods which make little use of the corn input and are therefore corn saving with regard to C. External rent occurs when the run to reach the normal rate of pro…ts is won by an iron method D. Then method D operates side by side with method C, and the production of iron is progressively transferred from C to D. As each ton of iron produced by means of D instead of C saves corn, the net product of corn increases for an unchanged gross production. The new long-term equilibrium is made of two iron methods C and D operating jointly, while corn is produced on a fully cultivated land. The rise in the price of corn sustains the payment of a positive rent.

To illustrate the phenomenon, consider a basic bisector model with a given corn method on a homogenous land and two iron methods:

(method C) 2 qr. corn + 1 labour ! 1 t. iron (5) (method D) 1 qr. corn + l labour ! 1 t. iron (6)
where the input labour l of method D is great enough (in that example, iron is not an input of its own production: this is a device to simplify calculations, but iron is a basic commodity as soon as it is used to produce corn). Method C is operated for low levels of demand because it is cheaper than D when the price of corn is low (l great enough). When the demand for corn increases and land is fully cultivated, the price of corn rises until method D becomes pro…table. Methods C and D operate jointly in the new equilibrium, with a progressive transfer of the production of iron. Such a coexistence is reminiscent of intensive cultivation but takes place outside the branch in which scarcity occurs.

In more complex economies, the substitution e¤ect may also take place in agriculture (joint use of two rice methods to increase the production of corn), and the direct and indirect interdependencies between industries are so complex that the emergence of an external rent is impossible to predict. [START_REF] Saucier | Le choix des techniques en situation de limitation de ressources[END_REF] showed that, when the response to the scarcity of corn leads to a progressive transfer of the production of rice, a rice land cultivated at low levels of demand may not be cultivated at higher levels. The phenomenon constitutes another critique of the notion of order of cultivation (for a given rate of pro…ts). Similarly, a positive rent may vanish when demand increases.

The economic consequences of external rent are much more dramatic for Ricardo's construction than Saucier suggested: the corresponding equilibrium is not reducible to a single-product system. If the rate of pro…ts is zero, the prices of corn and iron in terms of wage are calculated as the solution to the equations

2p c + 1 = p i (7) p c + l = p i (8)
The prices once known, the level of the rent is determined by the agricultural method. Even if the usual two-step procedure (…rst the prices, then the rents) works, the formal solution (p c ; p i ) to ( 7)-( 8) cannot be interpreted in terms of labour values since the conditions of production of corn do not intervene in the determination of its value. An economy reduced to methods C and D could not reproduce itself: the equilibrium is of a non-Ricardian type. When the rate of pro…ts r is positive, the prices in terms of wage are de…ned by the equations

2p c (1 + r) + 1 = p i (9) p c (1 + r) + l = p i (10)
from which there follows that the price of iron is constant and that of corn decreases with the rate of pro…ts (p i = 2l 1; p c = (l 1)=(1 + r)). The real wage thus increases with the rate of pro…ts. The notions of external rent and non-Ricardian equilibrium often play a hidden role in the economic literature on rent:

-Salvadori (1986) established an existence result for long-term equilibria with scarce resources. No agent is in charge of checking whether the number of operated industrial processes coincides with that of industrial goods. Ricardian and non-Ricardian equilibria are interwoven, with switches from a type to the other when demand changes. There are strong reasons to think that non-Ricardian equilibria are frequent in complex economies.

-Bidard (2010) intended to elaborate a general theory of intensive proper for a given real wage, a unique quality of land and several processes in agriculture and industry. Once the real wage is incorporated into the input matrix, there is no longer explicit labour, but a uniform rent appears in the price equations. The formal similarity with a single-product economy, with land and rent instead of labour and wage, seems perfect. One can draw the family of all r curves, and the cost-minimising combinations of methods are those which lie on the upper envelope. Moreover, as two agricultural methods produce the same good, only the switch points on the envelope matter. The conclusion seems to justify Sra¤a's statement: 'In the case of a single quality of land, the multiplicity of agricultural products would not give rise to any complications'(PCMC, Section 89). However, the construction relies on the implicit hypothesis that one method is operated in each branch, which is not the case for productive systems with land in a non-Ricardian equilibrium.

-Similarly, the restrictions mentioned at the end of Section 2 in the theory of extensive cultivation stem from the necessity to eliminate non-Ricardian equilibria: the uniqueness hypothesis on the industrial methods discards the coexistence of industrial methods producing the same good; the uniqueness of the agricultural good discards the joint use of two marginal rice methods in order to increase the net product of corn.

Is there a way to extend the expected results to several agricultural goods? A natural idea is to return to Ricardo and to assume that the agricultural methods can be classi…ed according to the amounts of capital goods and labour employed per acre. Even then, the coexistence of two marginal rice methods in order to increase the production of corn cannot be excluded. Moreover, Ricardo did not set a similar hypothesis on industrial methods and, on the contrary, what is nowadays called the Ricardo e¤ect points at the substitutability between capital and labour in industry, as in the above numerical example (5)- [START_REF] Kurz | Theory of Production[END_REF]. Non-Ricardian equilibria cannot be excluded except in very speci…c con…gurations, and Ricardo's project to reduce the study of an economy with land to that of an economy without land fails in their presence.

Conclusion

The aim of Chapter 2 of the Principles is to consider 'whether the appropriation of land, and the consequent creation of rent, will occasion any variation in the relative value of commodities, independently of the quantity of labour necessary to production'. For contemporary economists, a similar question can be addressed to the theory of prices of production. Ricardo's and Sra¤a's idea is that the presence of lands has no major analytical consequence because one can get rid of rent by considering the marginal methods of cultivation. By contrast, our main conclusions are:

-As far as one considers extensive cultivation only, the elimination of rent from the analysis of value is limited to speci…c cases. Ricardo's reference to a natural order of cultivation, which Sra¤a criticised, plays a central role in that operation.

-In the case of intensive cultivation, a similar hypothesis is also required, otherwise the reduction to a single-product system is not possible and the trade-o¤ property does not hold, even in a corn-land model.

-Ricardo and Sra¤a omitted the existence of a third type of rent. External rent occurs when the number of marginal corn methods does not allow to determine the price of corn and the rent. However, since another commodity is produced by two marginal methods (or by two methods, for an industrial commodity), the number of equations remains su¢ cient to determine prices. As the conditions of production of corn play no role in the determination of its price, the structure of these equations is deeply di¤erent from those associated with single-product systems and the extension of the trade-o¤ property cannot be expected. The question of the impact of taxation studied in Chapters 8 to 18 of Principles should also be revisited.

These conclusions cast doubt on the relevance of the strategy adopted by Ricardo. Ricardo considered the question of rent as a main economic, social and political issue, but his theoretical message is that rent is analytically inessential. As the interactions between prices and rents are more complex than he thought, the question of the grounds of the Ricardian dynamics remains open.

In this respect, we disagree with Fratini's (2012) critique of Ricardo. Fratini starts from Sra¤a's formalisation, which does not coincide with Ricardo's approach, and fails to identify the capital invested in method as the marginal capital to which Ricardo refers.


Irfan Akbar Kazi

Suzanne Salloy

Dorothée Rivaud-Danset

Pierre Blanchard

Dominique Lacoue-Labarthe

Contagion effect due to Lehman Brothers' bankruptcy and the global financial crisis -From the perspective of the Credit Default Swaps' G14 dealers

Keywords: Financial Crisis, Contagion, Credit Default Swap, Lehman Brothers, Asymmetric Dynamic Conditional Correlation. JEL classification: G01, G15, G21, G33 Crise financière, Contagion, Credit Default Swap, Lehman Brothers, Corrélation Conditionnelle Asymétrique Dynamique. Classification JEL: G01, G15, G21, G33

, we examine if there is contagion during the global financial crisis, following Lehman Brothers' bankruptcy of September 15 th , 2008. The main contribution of this article is to analyze if the interdependence structure between the G14 banks changed significantly during the crisis period. We try to identify the banks which were the most or the least affected by losses induced by the crisis and we draw some conclusions in terms of their vulnerability to financial shocks. We find that all banks became highly interdependent during Lehman Brothers' bankruptcy (short term impact), but only some banks faced high contagion during the global financial crisis (long term impact). Regulators who try to reinforce banks' stability with the Basel 3 reforms proposals should be interested by these results.

Introduction

The common traditional distinction between risks, illiquidity and insolvency risk is attributed to Bagehot (1873) and it applies to traditional banking, and especially commercial banks. This typology of risks is important in terms of policy implications as central banks' intervention should be discretionary in function of the risks confronted by the banks (Bagehot, 1873). Central banks should distinguish between institutions that are insolvent and those that are merely illiquid. They should lend their hand to solvent financial institutions even if they face liquidity problems. In the case of insolvency, central banks should not intervene as the lender of last resort, but let the financial institutions go into bankruptcy. However, the distinction between illiquidity and insolvency is sometimes hard to define and there exist a strong interaction between illiquidity and insolvency risks (see for example [START_REF] Frank | Transmission of Liquidity Shocks: Evidence from the 2007 Subprime Crisis[END_REF]. Insolvency risk could be the consequence of decrease in asset prices that could then trigger liquidity crisis. Bagehot's distinction ignores market factors that impact illiquidity and insolvency risks and seems irrelevant in the case of the global financial crisis of 2008-

2009.

The global financial crisis is not similar to past crisis (see [START_REF] Dungey | The Tsunami: Measures of Contagion in the 2007-2008 Credit Crunch[END_REF] among many others). This crisis appears to be the most devastating since those that have preceded the Great Depression in the United States and the banking crisis prior to the First World War. Traditionally, banking crises occur when depositors queue up to withdraw their money in a panic [START_REF] Diamond | Bank Runs, Deposit Insurance, and Liquidity[END_REF]). These banking crises appeared with a run on the bank, but they had evolved in time and incorporated different types of risks. Northern Rock in September 2007 went through a 'bank run'. This 'bank run' was a consequence of the difficulty faced by Northern Rock's access to interbank market during the subprime mortgage crisis. A crisis of confidence appeared as depositors were aware of the funding difficulties faced by the bank. This was one of the dramatic indications that difficulties at the beginning of the crisis were spreading beyond the United States. The 'traditional' banking system in which commercial banks used to hold loans until they were repaid transformed into 'modern' banking in which all sorts of loans were pooled together, tranched, and then resold via securitization. This financial innovation was called the 'originate and distribute' model (see for example [START_REF] Brunnermeier | Deciphering the Liquidity and Credit Crunch 2007-2008[END_REF]). This financial innovation ultimately led to a decline in lending standards contrary to its first function of making the banking system more stable by transferring risk to those who were capable to bear it.

During the subprime crisis, 'modern' runs occurred in financial markets, especially within the interbank and money markets, mainly because of financial innovations. Banks stopped granting credit to each other because of their fear of contaminated subprime loans. The fear that the securities issued against mortgage loans, serving as collateral, to their own financing may have to be written off.

Therefore, it is important to take into account the new risks associated with crisis that heavily depend on the development of financial innovations, such as credit derivatives. Credit derivatives are financial assets whose payoffs depend on credit risk of a financial institution. The most popular credit derivative during the subprime crisis was the Credit Default Swap (now on as CDS). CDS account for approximately 70 percent of total credit derivatives negotiated all over the world. CDS contracts are financial instruments to hedge the default risk born by creditors and to transfer it to other agents. Three agents intervene: the buyer (assured), the seller (insurer) and the reference entity (borrower of the underlying asset). The CDS contract allows the buyer to hedge against the default risk of the reference entity and the seller to get compensation to ensure this hedging. Many financial institutions or insurer companies during the subprime crisis, such as American International Group (now on as AIG) or Lehman Brothers (now on as LB) faced a sudden lack of funding because of their positions (as seller) on the CDS market. The bankruptcy of AIG would have generated great financial difficulties for the buyers, who had their major investments in American commercial banks. LB was a major dealer on the CDS market with positions as seller as well as reference entity. In the case of AIG, it was appealing to be a net seller of CDS as its' insurance were subject to different prudential regulations and could find interest in bearing credit risk if compensation was appealing. With the default of a major counterparty on the CDS market, financial institutions ran the risk of illiquidity. The failure of certain financial institutions would have lead to systemic risk.

The CDS market could become contagious, as opposed to its first function of diversification of risks. Four factors may ignite contagion in this market. The first vulnerability factor in this market is due to the positions' imbrications. Financial institutions in this market have to hold a reverse position to cancel their first position. The second factor is a huge concentration of risks due to the exposition of financial sector to this market. The G14 banks' dealer1 (Bank of International Settlements) realized the majority of transactions in this market. The third factor is the opacity of the market. It can create doubts about the capacity of sellers to honor their contracts. The last factor is the counterparty risk, or credit risk. The bankruptcy of a major financial institution (now on FI) can create difficulties for other FI because of their mutual positions. Moreover the fact that the notional value of credit default swaps was a large multiple of the value of the underlying bonds created the danger of a domino effect if one large issuer of default swaps was to fail. With the subprime crisis, counterparty risk associated with CDS clearly appeared and financial institutions which were first considered as safe appeared as risky. Doubts about the capacity of CDS's sellers to insure their contracts appeared as a factor of contagion.

The nature of credit risk changed due to securitization. Before the financial engineering era, credit risk was sustained by banks themselves while granting loans. Banks were subject to prudential regulations such as capital requirements. Securitization which developed in the 1990s, allowed the bank to pool heterogeneous loans, trench them, and resell the same to other investors on financial markets with the intervention of brokers. Banks became capable of transferring the credit risk and hence required lesser capital to meet regulatory requirements. Since derivative markets are over-thecounter markets (OTC), they involve the difficulty of estimating credit risk even if CDS premiums depend on the default probability of a reference entity. Credit risk spread and moral hazard allowed banks to become less prudent. The banks now knew, how to sell the credit, and were not obliged to keep them on their balance sheet. It is due to this fact that we focus on credit risk and measure contagion effect on the CDS market.

Liquidity risk did not draw much attention from regulators compared to credit risk or market risk. With the subprime crisis, managing liquidity risk became a priority2 . In a modern market-based financial system, the vehicle of contagion is the price changes, just not only the default on loans [START_REF] Shin | Liquidity and Financial Contagion[END_REF]. The first factor that caused crisis was the sudden fall in house prices. Thus, mortgages default started increasing due to the fact that these subprime loans were issued with variable interest rate, relax lending practices, and without borrower income assessment to support such circumstances. The subprime mortgages fell in value and they became volatile and more difficult to price. Banks possessed most of such financial derivatives that were mainly financed by leverage (a capital structure that heavily relied on short-term debt). As a consequence, banks became illiquid.

Further, as banks tried to sell out their positions, prices decreased and concerns about illiquidity turned to insolvency. Banks had to face decrease in their asset value which did not match the liabilities. Bank runs started and the interbank market froze up. Banks refused lending each other and preferred hoarding their funds. Schema 1 shows how the risks evolved during the subprime crisis.

In this paper, we emphasize the impact of Lehman Brothers (LB)'s bankruptcy on 15 th September 2008 on the CDS market. This date is largely accepted by researchers, policy makers and the practitioners as the starting point of the global financial crisis. For some authors, this bankruptcy led to systemic risk [START_REF] Acharya | The Financial Crisis of 2007-2009: Causes and Remedies[END_REF]). We focus on LB's bankruptcy since it was a major dealer in the CDS market. The default of a large insurer such as LB could lead to a domino's effect which became evident just after its announcement of bankruptcy. This announcement gave birth to fears concerning the capacity of the CDS market to bear such shocks. The questions we investigate in this paper are as follows: First, did the interdependence structure among banks remain constant or did it change with time? Second, were all banks affected with the same magnitude during the global financial crisis? Third, did Lehman Brothors' failure have a short term or long-term impact on time varying pair correlations? To answer these questions, we consider two event windows. A short event window of four weeks following Lehman's collapse was considered since Lehman announced its bankruptcy on September 15, 2008 and CDS were settled through an auction three weeks later on October 10, 2008. A longer window of 37 weeks following LB's bankruptcy was considered in order to capture the impact of the global financial crisis that ended on May 27, 2009 according to Greenspan. The definition of contagion used in this paper is similar to the literature (see for example [START_REF] Forbes | The "Big C": Identifying Contagion[END_REF]Rigobon (2000, 2002), Coudert and Gex (2008), [START_REF] Yiu | Dynamic Correlation Analysis of Financial Contagion in Asian Markets in Global Financial Turmoil[END_REF][START_REF] Tamakoshi | A Dynamic Conditional Correlation analysis of European stock markets from the perspective of the Greek sovereign debt crisis[END_REF]). Contagion is defined as a significant increase of dynamic conditional correlations between banks' CDS during the GFC relative to the correlations during the pre-crisis period. We measure contagion with conditional correlations following Forbes (2009). Contagion in this paper is measured from Lehman Brothers' bankruptcy to other banks. No assumption is made concerning the contagion effect among the other banks. It is a measure of the impact of Lehman Brothers' bankruptcy on conditional correlation of CDS between each couple of banks.

This paper makes several contributions to the existing literature on contagion effect during the global financial crisis. First, as far as we can tell, this is the first attempt to empirically model the impact of LB's bankruptcy on the CDS market with the Asymmetric Dynamic Conditional Correlation (ADCC) model. Empirical studies focusing on financial institutions' CDS mainly concentrated on principal component analysis and dynamic panel [START_REF] Eichengreen | How the subprime crisis went global: evidence form bank credit default swap spreads[END_REF] or robust panel estimates [START_REF] Raunig | Are banks different? Evidence from the DCS market[END_REF]. As Forbes (2009) stated, DCC is a good method to measure contagion.

Second, this study specifically addresses the issue of contagion from a microeconomic perspective and not a global level. By focusing directly on financial institutions' CDS, we measure bank contagion and not financial or global contagion as previous literature did. Many studies focus on stock market indices or CDS sovereign bonds. Our methodology focuses on individual banks, thus allowing us to distinguish between the most affected FIs instead of taking a global approach to countries or market indices. Besides, estimating the market assessment of bank credit risk or default is relevant to policy implications and more especially to macro prudential policies. Regulators who try to reinforce banks' strength with the Basel 3 reform proposals should be interested by this methodology. For policymakers, the predictions of the dynamic correlation between banks could be a useful tool for preventing systemic risk during crisis period. Third, by using multivariate GARCH (Generalized Auto-regressive Conditional Heteroskedasticity) models instead of the univariate GARCH model, we jointly analyze the volatility of two financial institutions and assess the links between these two series. The GARCH framework allows for the modeling of the heteroscedasticity of the data, in addition to interpreting conditional variance as a time-varying risk measure. [START_REF] Engle | Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models[END_REF] proposes the Dynamic Conditional Correlation (DCC) model to alleviate the dimensionality problem of the general Multivariate GARCH (MGARCH) model. Engle's DCC model comprises two steps, fitting each series to univariate GARCH model to get the residuals and then deriving the dynamic conditional estimates. This model was modified by Cappiello, [START_REF] Capiello | Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns[END_REF], the Asymmetric Dynamic Conditional Correlation (ADCC) to allow for the possibility of having asymmetric impact of positive innovations and negative innovations on the dynamics of the conditional correlations. As the DCC model by [START_REF] Engle | Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models[END_REF] can lead to inconsistency problem with the DCC estimator (Aielli, 2008), we thus decide to implement the ADCC model by Cappiello, [START_REF] Capiello | Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns[END_REF] which allows incorporating heterogeneity in the data, such as asymmetric news impact and no smoothing parameters for all pairs of variables.

The rest of the paper is organized as follows. In the second section, we focus on the literature review. In the third section, we develop the database. In the fourth section, we present the econometric methodology. In the fifth section, we present the main empirical results. In the sixth section, we conclude and present future areas for research.

Risk typology and literature review

Risk typology

We review the risks occurring during the global financial crisis (Table 2). We identified types of financial risks: insolvency risk, illiquidity risk and credit risk. Some variables depending on the macroeconomic environment can lead to a modification of those risks, they are mainly prices and interest rates. Systemic risk is also detected during the subprime crisis.

The 2008-2009 financial crises led to a differentiation in illiquidity risk (Brunnermeir, 2009):

1/funding liquidity (individual liquidity risk) and 2/market liquidity (systemic liquidity risk). Funding liquidity appears when a bank is unable to easily obtain funding (for instance, at excessive costs, and/or with a limited amount) from the interbank market. Market liquidity risk appears when a bank is unable to sell its assets at or near their fair value due to market disruption or when a bank's reputation has been undermined. Transactions for complex financial products occur in over-the-counter (OTC) markets, thus these markets are not centralized making them difficult to evaluate. They are valued through models that incorporate product characteristics. With the crisis, these models did not give prices any longer for the underlying assets which made banks unable to value some of their financial assets / products. Funding illiquidity risk then materialized and banks became concerned about their future access to capital markets and started hoarding funds. As a consequence, banks tried to sell off some of their positions. This effect was reinforced by the fact that banks heavily relied on leverage, such as short-term borrowing. Market illiquidity risk was observed through a sharp drop in asset prices. The market liquidity crisis is a new risk that appeared with the crisis and can be viewed as one factor of contagion. Central banks clearly intervened from summer 2007 following the freeze on the interbank market 3 . Usually financial institutions could obtain funds at short term on this market. The risk not considered beforehand by financial regulators in Basel 2 before the crisis, became important with the request of international criteria for managing liquidity risk. The importance of an increase in 3 Central banks have extended the nature of collateral for mortgages loans and started granting exceptional loans to investment banks and insurance not submitted to the same regulation. Meanwhile, interest rates were lowered significantly in order to restore bank profitability. liquidity risk during the crisis entailed many interventions of central banks to inject funds in order to avoid a freeze on the markets.

Risk

Name Definitions

Financial risks

Illiquidity risk (market liquidity and funding liquidity)

A financial institution even if solvent either does not have enough financial resources to allow it to meet its obligations when they are due, or can obtain such funds only at excessive cost (Brunnermier and[START_REF] Brunnermeier | Market liquidity and funding liquidity[END_REF]Brunnermier (2009).

Insolvency risk

A financial institution has more liabilities than the reasonable market value of its assets. In this case, the bank is insolvent.

Insolvency risk can result from illiquidity risk.

Credit risk (or counterparty risk)

The counterparty may face a default and failing to repay its debt. This risk becomes harder to evaluate with the development of complex financial products due to securitization.

Macroeconomic risks

Interest rate risk

Changing the value of an investment due to a change in interest rate. The subprime loan holders had variable interest rates.

Price changes risk

The collapse of a market leads to a decrease of asset prices. In general, we observe a risk premium variation [START_REF] Shin | Liquidity and Financial Contagion[END_REF].

Contagion risk

Systemic risk

The widespread failures of financial institutions or freezing up of capital markets that can substantially reduce the supply of capital to the real economy [START_REF] Acharya | The Financial Crisis of 2007-2009: Causes and Remedies[END_REF].

During the financial crisis, after prices decreased and financial products could not be valued, banks tried to shrink their balance sheets and deleverage as they discovered their capital eroding.

There was a transformation of illiquidity risk into insolvency risk (i.e. bank assets were not enough to match the liability side).

The systemic risk is the consequence of higher interconnection between FIs. The bankruptcy of a FI could lead to the bankruptcy of the whole financial system because of the linkages between the FIs. Systemic risk may imply 'Too Big To Fail' label for institutions. This designation can become exante costly since it induces moral hazard with banks becoming less prudent regarding risks they face.

Systemic risk ex-post can be the consequence of several mechanisms that amplify and propagate liquidity shocks across financial markets. This transmission can appear directly between banks' balance sheet, and indirectly through asset prices (Adrian and Shin, 2007).

Review of literature

Table 3 synthesizes the principal studies which deal with contagion, either related to finance or banking. Assessing contagion through the use of correlations is increasingly used in literature. From unconditional correlations to dynamic conditional correlations (DCC) by [START_REF] Engle | Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models[END_REF] and to Asymmetric DCC specification by Cappiello et al. (2006), techniques to detect contagion through correlation have improved. This last specification allows taking into account the dynamics of correlation and structural breaks. The first specification by [START_REF] Engle | Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models[END_REF] implies that the conditional correlations are mean reverting to their constant long-run unconditional average, so that the shock is transitory. Under the DCC specification by [START_REF] Capiello | Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns[END_REF], the subprime crisis can be modeled as a structural break in the data generating processes, rather than a transitory shock. Aielli (2008) shows that the DCC estimator model by [START_REF] Engle | Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models[END_REF] can be inconsistent and lead to the existence of bias in the estimated parameters of the model. Aielli (2008) shows that the bias depends on the persistence of the DCC dynamic parameters and that the sample estimator of the correlation matrix of the standardized residuals used in the second step of the DCC estimation method is inconsistent, thereby also affecting the consistency of the third step. [START_REF] Frank | Transmission of Liquidity Shocks: Evidence from the 2007 Subprime Crisis[END_REF] also prefer the DCC estimation methodology of Cappiello et al. (2006). Other versions of the DCC model have been implemented such as DCC-EGARCH (Alraigbat ( 2011)), G-DCC [START_REF] Hafner | A Generalized Dynamic Conditional Correlation Model: Simulation and Application to many assets[END_REF]), DCC-GARCH [START_REF] Wang | The integration of the credit default swap markets during the US Subprime crisis: Dynamic correlation analysis[END_REF]). These studies generally use the log likelihood estimator which allows for consistent standard errors robust to non-normality.

In order to study financial contagion, researcher use stock market returns (see for example estimate the correlation between the Asian factor and the US stock market. They find evidence that there is contagion from the US to the Asian markets. [START_REF] Frank | Transmission of Liquidity Shocks: Evidence from the 2007 Subprime Crisis[END_REF] with ADCC-GARCH model of Cappiello et al. (2006) show that the interaction between U.S. market and funding illiquidity increased sharply during the subprime crisis and bank solvency became an important issue. [START_REF] Wang | The integration of the credit default swap markets during the US Subprime crisis: Dynamic correlation analysis[END_REF] by using the DCC of [START_REF] Engle | Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models[END_REF] and data on the CDS sovereign bonds find that LBs' bankruptcy strengthened the integration between sovereign bond CDS of developed economies with the USA. In terms of the driving factors of this correlation, they conclude that CDS bonds markets were mainly driven by USA interest rates. They focus on the unconditional correlations of weekly changes in CDS spreads between the US and others markets and on the conditional correlations between US and non-US CDS spreads. By looking at the DCC series for each pair of countries, they find that the pattern of correlation changed significantly before and after the LBs' bankruptcy. They conclude that LBs' bankruptcy was seen as a major event during the crisis and contributed to the integration of the CDS markets amongst advanced economies. [START_REF] Raunig | Are banks different? Evidence from the DCS market[END_REF] with a different method of fixed effects and random effects focusing on individual bank data of CDS, find that after August 2007 investors increased their perception of risk concerning banks. [START_REF] Eichengreen | How the subprime crisis went global: evidence form bank credit default swap spreads[END_REF] with principal component analysis and CDS data on individual banks show that common factors for banks' CDS play a major role in explaining the spillover effects between banks. Finally these studies have the common point of dealing with the impact of the 2008-2009 financial crises. 2009). The first moment is positive for all banks for the whole period, as well as for the pre-crisis period. On the contrary, it is negative for three banks (GS, JPM and WF) for the GFC period, CG and RBS got even more positive returns, a sign that their CDS premiums were traded with a higher probability of default.

The data

These FI had shorted considerable amount of Collateralized Debt Obligations before the crisis and even if they had subscribed insurance by buying CDS in case of default, this did not reassure investors. Standard deviation is higher for all banks during the GFC than during the pre-crisis period, a sign of higher tension and volatility in the market. By looking at the kurtosis and the skewness coefficients, 10 banks have lower value of kurtosis and skewness during the GFC compared to the precrisis period. This is not the case for 4 banks (GS, MS, UBS and CS). Higher values for the second moment during the GFC period rather than the tranquil period are also confirmed by the maximum values which are higher during the GFC.

Methodology

We study time varying correlations among the weekly returns of the CDS premiums of G14 banks from January 2004 to May 2009. We adopt a three stage approach.

First, we estimate the conditional variance for each of 14 CDS returns series using a univariate EGARCH specification and selecting the best EGARCH (p,q) models 5 . By using an EGARCH specification for the variance conditional equation we want to test if there is any asymmetry on the conditional variance due to a bad news. If so, a bad news would have a more impact on the variance than a good news. The EGARCH(p,q) framework may be presented as follows :

(1) Mean equation:

∑ (1)
(2) Conditional variance equation:

log ∑ ∑ log (2)
In our econometric framework the estimated conditional variance equation is specified as: Given the standardized residuals and the standardized negative residuals, the dynamics of the conditional correlation matrix denoted by in the asymmetric DCC is given by the following two equations:

log ∑ ∑ log (
1 ∑ ∑ ∑ ∑ ′ ∑ ∑ (4)
5 To determine the lag structures (p,q) we use Akaike, and Schwarz / Bayesian information criteria. It should be noted that Akaike criterion overshoots when p is increased (see Bierens (2009)). p and q are selected by minimizing AIC and BIC. * * (5)

Where P E ε ε , N E η η′ and * t Q is a diagonal matrix with square root of i-th diagonal element of conditional correlation matrix on its i-th diagonal position.

If N equals zero, then the ADDC becomes a DCC model.

For ADCC(1,1), the equation ( 4) may presented as follows:

1 * (6)
The log-likelihood of the estimators of the asymmetric DCC is identical to the case of original DCC except the modification in . Denote to be the vectors of parameters to be estimated, and the loglikelihood is given by:

∑ log 2 2 (7)
Where n and T are the number of series (in our case 14) and the number of observations, respectively.

We note , the estimated DCC coefficient between banks i and j at time t.

Third, we model the estimated DCC coefficient , for each couple of banks i and j as an AR model. Specifically the dummy variable signifying the global financial crisis (GFC) (from September 17, 2008 to May 27, 2009 which represents 37 weeks) is included in order to test whether the GFC significantly altered the dynamics of the estimated conditional correlations between the G14 banks.

We estimate the following model 1:

, ∑ , (8)
Where , is the estimated dynamic conditional correlation coefficient between banks i and j at time t. , and are the estimated coefficients respectively to the constant term, the lagged ADCC coefficient and the GFC dummy variable.

This model is modified to take into account a shorter window event focusing on Lehman Brothers' bankruptcy (now on as LBB). We consider a dummy variable equals to one for the period from September 17, 2008 until October 8, 2008 (4 weeks). The model 2 estimated is the following:

, ∑ , (9)
With as the estimated coefficient associated with the dummy LBB variable.

In order to capture the short term impact of LBB the window size is set equal to four weeks. The choice of four weeks is based on the fact that it took exactly four weeks between the declaration of Lehman Brothers bankruptcy and its auction i.e. October 10 2008. On the other hand, the event window of 37 weeks reflects the long term impact on the market due to GFC.

Empirical results

We present the results of the three steps presented in section 4. First we deal with EGARCH specification, second we focus on the estimation of asymmetric DCC model and third we present the results of the AR model for the estimated asymmetric dynamic conditional correlation.

In the first step, we estimate conditional variances for each bank using EGARCH methodology of Nelson (1991). The results are presented in table 5. We find that most of the time the mean equation is not significant for our banks. This result is in line with the literature as in Cappiello et al. ( 2006) and [START_REF] Tamakoshi | A Dynamic Conditional Correlation analysis of European stock markets from the perspective of the Greek sovereign debt crisis[END_REF]. However, the ARCH and GARCH terms of the variance equation are highly significant with the asymmetric parameter significantly negative for 9 banks which means that the model fits well the data. We test heteroscedasticity of the residuals with an ARCH test (Engle (1982)) and we test residuals for not being autocorrelated with the Ljung-Box and Mc Leod-Li tests. The results suggest the acceptance of null hypothesis of no autocorrelation up to 20 lags for standardized residuals and standardized residuals squared. Economically, this means that the standard deviation of the residuals do not depend on its past values, so that there is no persistence of shocks. As our analysis focuses on the dynamics of correlations of CDS returns, the well-fitted variance equations allow us to conclude that our EGARCH models fit the dataset in a very reasonable way.

In the second step, we deal with the estimation of the asymmetric DCC models. Table 6 presents the estimates of ADCC model. Both the estimates on the parameter of standardized residuals (AFIX), and the parameter of innovations in the dynamics of the conditional correlation matrix (BFIX) are statistically significant. AFIX means that the effect of past shocks is significant and BFIX that that effect of past covariance is significant. However, the estimate on the parameter of the standardized negative residuals (GFIX) is not significant even at 10% level for all the banks which means positive and negative news would have the same effect on the conditional correlation of CDS returns.

According to the literature, the non-significance of the asymmetric parameter is common to empirical results, [START_REF] Yiu | Dynamic Correlation Analysis of Financial Contagion in Asian Markets in Global Financial Turmoil[END_REF] and Cappiello, [START_REF] Capiello | Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns[END_REF]. Figure 3 describes the estimates on time-varying conditional correlations between each pair of banks. The figure shows the timevarying pattern of correlations between banks. For all graphs, we see a peak in correlation during the GFC that started with LB's bankruptcy.

In the third step, we present the results of AR model for the estimated dynamic conditional correlation. Our last step is to apply AR(1) with a dummy variable for the GFC period to the evolution of the estimated DCC. Table 7 shows the estimated parameters of AR equations of the estimated conditional correlations. We look at the results for model 1. We interpret three parameters: 1/ The constant term whose meaning is the link between pairs of banks. It can be either positive or negative.

2/ The coefficients of the AR term are significant and since they are less than unity, they indicate the stationary of our data. 3/ The coefficients of the GFC dummy are also found to be significant for some banks, which means some banks are subject to the effects of the GFC while other are not. The relative high level of R 2 ensures the quality of the adjustment of the regression.

Four banks appeared vulnerable to the GFC since they have positive significant dummy crisis coefficient; GS, MS, BOA and UBS. For instance, they have 10 out of their 13 total correlations that had been significantly impacted by the GFC. More precisely, the pair correlation increases in the GFC more sharply than in the pre-crisis period. Goldman Sachs was severely affected by the crisis, for instance its correlation with BNP Paribas increased by 1.07% during the GFC, its correlation with HSBC increased by 1.09% and with UBS by 1.01%. Bank of America also had higher correlations during the GFC. Its correlation with HSBC increased by 1.03% during the GFC and its correlation with Goldman Sachs increased by 0.61%. UBS correlation with Goldman Sachs increased by 1.01%

during the GFC, and with Morgan Stanley by 1.06%. Then, we find HSBC and RBS, these two British banks have been impacted, with 7 dummy GFC coefficients significant. We have then Citigroup, Deutsche Bank and Barclays and the two French banks BNP Paribas and Société Générale. And finally the less affected banks during the GFC are JP Morgan, Wells Fargo and Credit Suisse. For JP Morgan and Crédit Suisse, 3 out of 13 of their ADCC increased significantly during the GFC (and respectively 4 for Wells Fargo) but they had non-significant increase in their correlation with other banks.

With the objective to test if the contagion that we observe during the GFC period was mainly due to Lehman Brothers' bankruptcy on September 2008 (see Table 7), we look at the results for model 2. We find that the dummy variable GFC is no more significant for majority of banks, even at the 10% level when adding the LBB's dummy variable. On the contrary, the dummy LBB variable is highly significant at 1% or 5% for all banks. This result shows that the significant increasing correlation for some banks found in the GFC is due to LBB. This analysis is supported by the graphics in Figure 3. We also observe that the ADCC increased significantly on September 17, 2008. This is the highest points in correlation for all banks during the period starting from 2004 until 2009. The ADCC in the graphs decreased in the shadow period of GFC. These results suggest that the effect on banks dynamic correlation during the GFC period is mainly due to LBB. The banks that do not have significant pair correlation during the GFC had managed to smooth the impact of LBB. These banks seemed less vulnerable to shocks and these results allow us to assess that all banks were not affected uniformly during the GFC.

We summarize these results in a symmetric matrix in tables 8 and 9. These tables synthesize the results of the effect of the GFC on banks pair correlations. On table 8, only are represented the significance level of the estimated coefficient associated with the dummy crisis, and on table 9 the estimated coefficient associated with the dummy global financial crisis.

For illustrative purpose, we propose a qualitative assessment on the probable link between the fundamentals ratios of banks and the probable impact of being affected by the crisis. While making some assumptions on the effect of the global financial crisis on the banks' pair correlation, we use a rating system from +++, ++ to +, which represents the qualitative likely degree of contagion during the GFC period. For instance, a rating of +++ corresponds to banks which are very likely to be impacted by the GFC and ++ for banks which are likely to be affected. On the contrary, a + rating means probably no impact of the GFC on the pair correlation. Our quantitative criteria for the qualitative rating are explained in table 11. By looking at the consolidated statements of the G14 banks at end of 2008, we consider four categories of ratios: asset quality, capital, operations and liquidity. In each of the four categories, we keep the most significant ratios.

Asset quality. We have the loan loss provisions/net interest revenue ratio. It measures a noncash expense for banks to account for future losses on loan defaults. Banks assume that a certain percentage of loans will default or become slow paying. We also have the ratio i:paired loans/gross loans which represents the loss the lender is likely to bear when he cannot collect the full value of the loan because the creditworthiness of the borrower has fallen.

Capital. We have the tier 1 ratio which measures the banking firm's core equity capital divided by the total risk weighted assets. The equity on total asset ratio helps to determine how much shareholders would receive in the event of a company-wide liquidation.

Operations. We have the net interest margin, a performance ratio that examines how successful a firm's investment decisions are compared to its debt situation. The Return on Average Asset (ROAA) is an indicator used to assess the profitability of a firm's asset. It is calculated by taking the net income and dividing by average total assets.

Liquidity. We have the net loans/total assets which measures the total loans outstanding as a percentage of total assets. And the liquid asset/total deposit and borrowings which measrues the liquid asset to total deposits and borrowings.

For each of the ratios, we used three intervals to translate the numerical value of the ratios into our system of rating from +++, ++ to +. Our three intervals are created by subtracting the maximum value of a ratio with its minimum value between banks. We then divide by three the amplitude of the values of the ratios to obtain equally weighted intervals. Finally we obtain three intervals for each of the eight ratios. For example, a bank which has a loan loss provisions/net interest revenue ratio comprised between 44.69% and 62.72% at the end of 2008 would be classify as having a high probability (+++) of being impacted by the global financial crisis. On the contrary, if its ratio is between 8.64% and 26.67%, it would be classify as probably no impact of the GFC (+). In the middle, a bank with a ratio comprised between 26.68% and 44.68% as having a medium probability of being impact by the GFC. The symmetric matrix in table 12 shows the probable impact of the GFC on the banks' correlations of the G14 banks using our qualitative rating. This table allows us to synthesize our assumptions concerning the most and the less affected banks by the GFC. In order to fill in correctly the matrix, we had a careful look on the balance sheets of the G14 banks of our sample at the end of 2008. We add then the number of + to create our proper qualitative rating for each couple financial institutions. Using the same method than for the ratio, we created three final intervals. Our final intervals are the following: for each couple of FI, the ones with more than 37 + are considered as having a very likely probability of contagion during the GFC. Each couple of FI with more than 30 + and less than 37 are considered as having a moderate probability of contagion and those under 31 + as having no probably impact of the GFC.

Table 12: Likely impact on pair correlations during the global financial crisis.

Source: Authors.

This table shows the probable impact of the global financial crisis on pair correlation. We use a rating from +++, ++ to + to measure the degree of contagion. +++ stands for a very likely impact of the GFC on the pair correlation, ++ stands for likely impact of the GFC and + stands for a no likely impact of the GFC. This table is a symmetric matrix with the banks in line and in column. Our empirical results (tables 7, 8 & 9) are consistent with our qualitative assessment (table 12). Our qualitative rating allows us to classify banks which were affected by contagion during the GFC based on their fundamental ratios. At the top of our qualitative rating, we find SG, RBS, HSBC, UBS, GS, BOA and BNP. In the bottom of our qualitative rating, we find DB, BAR, WF, C, MS, CS and JPM. Rational contagion during the GFC crisis with Lehman Brothers' bankruptcy is observed since the banks the most affected are also the one whose fundamentals ratios were most penalizing.

C GS JPM MS

We find evidence of interdependence due to Lehman Brothers' bankruptcy for all banks, but contagion during the global financial crisis is significant for some banks. We look at the subprime write downs and losses of Mortgage Backed Securities (MBS) and Collateralized Debt Obligation (CDO) during the crisis (Table 13). We find that the more the banks announced subprime writedowns, the more they are affected by contagion during the GFC. Citigroup, UBS, HSBC, Bank of America, Royal Bank of Scotland, Morgan Stanley and JP Morgan were the banks in the top ranking that announced writedowns and losses. These banks are the ones whose the number of pair of correlations increased significantly during the global financial crisis (except for JP Morgan). In the top down ranking of writedowns announcements, we find Deutsche Bank, Crédit Suisse, Wells Fargo, Barclays, Société Générale, BNP Paribas and Goldman Sachs. These banks were also the less affected by contagion in our model (except for Goldman Sachs).

Our empirical results are similar as [START_REF] Salloy | La Contagion bancaire informationnelle lors de la crise des subprimes : une étude sur les marchés boursiers européens et américains[END_REF]. The author finds rational contagion during the GFC especially due to Lehman Brothers' bankruptcy with some banks less affected than other. For instance, JP Morgan when studying contagion with abnormal returns did not show significant negative abnormal returns. In this study, the bank holding company resisted to the GFC. We also find consistent results with [START_REF] Acharya | The Financial Crisis of 2007-2009: Causes and Remedies[END_REF] who consider LB' bankruptcy as a triggering event for systemic risk. Also with [START_REF] Wang | The integration of the credit default swap markets during the US Subprime crisis: Dynamic correlation analysis[END_REF] who consider that LB had reinforced the integration between developed markets.

From our results, we distinguish the short term impact of LB's bankruptcy and the contagion.

While all banks were affected by LB's bankruptcy, only some went through contagion during the GFC. Higher level of correlations during the LBB is an important indication of systematic impact and increased interdependence among the banks. This result can be explained by the structure of the CDS market. Notional value of the CDS contracts was a large multiple of the value of the underlying, which created the danger of domino effect. If one large insurer of credit default swap such as Lehman

Brothers failed. This effect may have been exacerbated by the fact that the swaps were traded over the counter with limited liquidity and the absence of a clearing house mechanism. The authorities may have underestimated the threat from the CDS market by letting LB go into bankruptcy.

The factors that could explain our results are as follows: 1/ the nature of business of a FI:

Investment banks, universal banks and commercial banks are not regulated under same set of regulations. After the crisis, some investment banks were seen as too risky such as GS and MS and faced considerable amount of losses that they decided to transform into bank holding companies and access deposits on the wholesale market. In addition, investment banks generally carried out very complex credit operations off their balance-sheet, placing them away from investor control. 2/ Fundamental ratios: As revealed by our qualitative assessment, there is a link between the fundamental ratios of a FI and its degree of contamination during the crisis. The more robust banks are, the less they suffer due to crisis. 3/ Systemic risk is a global factor and cannot be completely attributed to FIs.

LBB could have made investors realize that the "Too Big To Fail" doctrine was not always on purpose and thus could have caused run on other FIs. 4/ The rating agencies that did not give sufficient warning made investors aware of the default risk of FI. Since rating agencies are paid by FIs for their rating, there exists a conflict of interest.

Conclusion

In this article, we applied Asymmetric DCC (Cappiello et al. (2006)) to model the interdependence structure between the G14 dealer banks for the period January 2004 to May 2009. By doing this, we answer three questions; First, did the interdependence structure among G14 banks remained constant or did it changed with time? Second, were all the banks affected with the same magnitude during the global financial crisis? And third, was the impact of Lehman Brothers' failure short term or long term on banks' correlation? Our approach is innovative as we are interested in contagion and correlation in the credit default swap market. A particular focus was placed on analyzing the impact of the financial crisis starting with Lehman Brothers' bankruptcy on the dynamics of CDS banks' correlations. We also propose a qualitative rating based on fundamental criteria to compare with our empirical results.

Concerning the results, we find that (i) the interdependence structure among the banks was dynamic and change with time; (ii) we find that all banks were affected by Lehman Brothers' bankruptcy which points towards significant short term impact of such an event, (iii) only some banks faced contagion during the global financial crisis. From the estimates of the asymmetric DCC models, we do not find evidence of asymmetry. Thus, the impacts of bad news and good news on the correlation between banks are not different. The AR model of the estimated DCC series is used to test the existence of contagion by including a global financial crisis dummy variable. We find no significant effect of the GFC for all banks. Some banks appeared as less vulnerable than other and did not seem to be affected by the crisis. We notice that the contagion during the GFC is mainly due to LBB. All the major dealers' banks in the CDS market did not react in the same way. The more robust banks could then constitute good opportunity for investors. Regulators who try to reinforce banks capital with the Basel 3 reform proposals should be interested by this result. For policy-makers, the predictions of the dynamic correlation between banks could be a useful tool for preventing systematic risk during crisis period.

of the leverage (short-term debt)

Illiquidity risk

Banks became illiquid

Funding illiquidity risk

Banks tried to sell off their positions

Insolvency risk

Drop in asset prices and assets < liabilities Market illiquidity risk

Credit risk

Freeze on the interbank market Panic on markets [68][69][70][71][72][73][74][75][76][77][78][79][80][81][39][40][41][42][43][44][45][46][47][30][31][32][START_REF] Athanasoglou | Bank-specific, industry-specific and macroeconomic determinants of bank profitability[END_REF][34][35][36][37][38]53 Std. Dev. 22 We recall that the pair correlations are symmetric. So reporting the estimated coefficients for banks i with j is the same that reporting the estimated coefficient for banks j and i.

  [START_REF] Naoui | A Dynamic Conditional Correlation Analysis of Financial Contagion: The Case of the Subprime Crisis[END_REF], and[START_REF] Alrgaibat | Dynamic Conditional Correlation and Asymmetric Volatility Phenomenon: Case Study in Major European Countries[END_REF] among many others) or exchange rate returns (see Celik(2012)). Yet, some studies focus on bank specific variables and look at banking contagion. Risks are identified, and proxy for each type of risk is captured with macroeconomic variables to control for shocks. Concerning the variables, credit risk is proxied by Credit Default Swaps (CDS), either bank CDS or sovereign bond CDS. CDS spreads reflect the market's assessment of credit risk(Longstaff et al. (2007)) and is an important indicator of the depth of the crisis[START_REF] Wang | The integration of the credit default swap markets during the US Subprime crisis: Dynamic correlation analysis[END_REF]. Eichengreen et al. (2009) using data on banks' CDS for 45 banks in developed economies, investigate the importance of common factors to explain their spreads. Athanasoglou and al. (2008) implement a series of bank-variables for Greece such as credit risk to assess the determinants of Greek commercial banks' profitability. Whereas, other studies focus on bank performance determinants or bank liquidity risk using a panel database. In this study, we focus on 2008-2009 financial crises and extend aforementioned studies. Tamakoshi et al. (2012) use the ADCC model to study the time-varying correlations between Greece and 6 other European countries from January 2007 to March 2011. They find that correlations showed significant decline during the sovereign debt crisis. Yiu et al.(2010) investigate contagion effects of global financial crisis in Asian markets by applying ADCC model. They perform principal components analysis to extract single latent factor to represent whole of Asia and with the ADCC they

,

  3) Second, we derive the time-varying conditional correlations with the asymmetric DCC model developed by Cappiello et al. (2006). The estimation procedure is close to the original DCC. The residuals obtained from the first step are standardized: , ,The negative standardized residuals for capturing asymmetric impacts of good and bad news are defined by:

Figure 3 :

 3 Figure 3: Weekly Asymmetric Dynamic Conditional Correlation between pairwise of banks.These are the graph of the asymmetric dynamic conditional correlation. The shadow area represents the GFC period starting on September 17th , 2008.

Figure

  Figure 3.1: ADCC between CG and other banks

Table 2 : Risks during the financial crisis. Source: Authors.

 2

  All the CDS premiums are extracted from Bloomberg and denominated in dollar currency in order to avoid any local currency effects such as inflation. Similar toCappiello et al. (2006) and Yui et al. (2010), we calculated Wednesday-on-Wednesday weekly returns, and we multiply them by 100 to express as percentages 4 . We use weekly returns because they are less noisy compared to daily data and in order to avoid any non-synchronous trading effect between countries. They also preserve the adequacy of data with sufficient frequency contrary to monthly data. Figures1 and 2show respectively CDS premiums and CDS returns for the G14 banks. Figure1shows that from 2004 until mid-2007 the CDS were relatively low driven by a market impact. From mid-2007, CDS premiums started increasing with investors' expectations of higher default. At the beginning of the GFC, we observe market downturn for CDS premiums. But early 2009, tensions on this market started again resulting in the rise of risk premiums.

	The G14 banks incorporated in our analysis are : Citigroup (United States), Goldman Sachs
	(United States), JP Morgan (United States), Morgan Stanley (United States), Wells Fargo (United
	States), Bank of America (United States), BNP Paribas (France), Deutsche Bank (Germany), HSBC
	(United Kingdom), Royal Bank of Scotland (United Kingdom), Société Générale (France), UBS
	(Switzerland), Barclays (United Kingdom) and Crédit Suisse (Switzerland). By focusing exclusively

Our dataset comprises of weekly returns of bank CDS premiums pertaining to G14 banks (281 observations per bank) from January 14, 2004 to May 27, 2009. The reference period is supposed to begin early January 2004 since the American business cycle was no more affected by the 2001 recession and this year highlighted the return of the US business cycle with a tightening monetary policy stance by the Federal Reserve. The end of the period is May 2009 since this is the official date of the end of the global financial crisis (Greenspan). The CDS premiums reflect the default risk on the FIs of the sample. on the G14 banks' dealer, we assume that G14 banks are most active on the CDS market and they should be affected by any market downturn. This assumption is also based on the large scale of exposure of these banks to the market events. Summary statistics of the weekly returns are presented in table 4. The descriptive statistics are presented for the whole period

(January 14, 2004 to May 27, 2009)

, the pre-crisis period

(January 14, 2004 to September 10, 2008)

and crisis period

(September 17, 2008 to May 27,

Table 11 : Rating criteria for qualitative assessment.

 11

	Source: Bankscope and authors.
	Categories	Ratios	value Expected		Qualitative rating
				+++	++	+
		Loan loss
		provisions/net interest	low	44,69% -62,72% 26,68% -44,68%	8,64% -26,67%
		revenue
	Asset quality
		Impaired loans/gross loans	low	2,78% -3,78%	1,78% -2,77%	0,77% -1,77%
		Tier 1 ratio	high	7,8% -9,63%	9,64% -11,46%	11,47% -13,30%
	Capital
		Equity/total asset	high	1,45% -4,29%	4,30% -7,12%	7,13% -9,97%
		Net interest margin	high	0,31% -1,26%	1,27% -2,21%	2,22% -3,17%
	Operations
		ROAA	high	-1,61% -0,87%	0,88% -3,34%	3,35% -5,83%
		Net loans/total assets	low	44,62% -66,44% 22,82% -44,61%	0,99% -22,81%
	Liquidity
		Liquid assets/total dep & Bor	low	51,12% -71,00% 31,26% -51,11% 11,37% -31,25%

Table 1 : Sample of the G14 dealers Financial Institutions.

 1

	Name	Short name	Country	Business type
	Citigroup	CG	UNITED STATES	Investment bank
	Goldman Sachs	GS	UNITED STATES	Investment bank
	JP Morgan	JM	UNITED STATES	Investment bank
	Morgan Stanley	MS	UNITED STATES	Investment bank
	Wells Fargo	WF	UNITED STATES	Commercial bank
	Bank of America	BOA	UNITED STATES	Universal bank
	BNP Paribas	BNP	FRANCE	Universal bank
	Société Générale	SG	FRANCE	Universal bank
	Deutsche Bank	DB	GERMANY	Investment bank
	HSBC	HSBC	UNITED KINGDOM	Universal bank
	Royal Bank of Scotland	RBS	UNITED KINGDOM	Universal bank
	Barclays	BAR	UNITED KINGDOM	Investment bank
	UBS	UBS	SWITZERLAND	Investment bank
	Crédit Suisse	CS	SWITZERLAND	Investment bank

Table 3 : Synthesis of the principal studies on contagion.

 3

	Authors	Problem	Data	Contagion	Sample	Period	Country	Risks	Variables to explain	Methodology	Estimator	Results
												Profitability of Greek banks was
	Athanasoglou, Brissimis and Delis (2008)	Examined the effect of bank-specific, industry-specific and macroeconomic determinants of bank profitability.	Individual	Banking	38 Commercial banks	1985-2001	Greece	Credit risk	Profitability ( ROA/ROE)	Dynamic panel	GMM	shaped by bank-specific factors, macroeconomic, and control variables that were not the result of
												bank's managerial decision.
	Eichengreen (2009)	Examined how the common factors influenced the movement of the 45 largest banks' CDS spreads at different time of the crisis.	Individual	Banking	45 developped banks	July 29, 2002-November 28, 2008 (weekly)	Developped	Credit rate risk risk/Liquidity risk/Interest	CDS of banks	1/Principal Dynamic panel Component Analysis. 2/	GMM	Common factors played a major role ==> irrational contagion
					41 banks
	Raunig and Scheicher (2009)	Examined how investors in the corporate debt market view banks.	Individual	Banking	(largest in EUR and USA) and 162 non-	January 2003-December 2007 (monthly)	US and EUROPE	Credit risk/Interest rate risk	CDS of banks	Fixed effect (FE) and random effect (RE) panel	Panel robust estimates	After August 2007 ==> investors viewed banks at least at risky as other firms.
					banks

Source: Authors.

Shen, Chen, Kao and Yeh (2009)

									Financing gap
		Causes of liquidity risk and the relationship between bank liquidity risk and performance.	Individual	Banking	12 commercial banks	1994-2006 (annual)	Developped Liquidity risk	ratio/short loans to term funding/net	Panel data instrumental/FE	2SLS	Liquidity risk decreased banks' profitability.
									customers
		Estimated the linkages between										The interaction between market and
	Frank, Gonzalez-Hermosillo and Hesse (2008)	market and funding liquidity pressures, and their interaction with solvency issues during the 2007	Global	Financial	5 US financial markets	January 3rd 2003 -January 9th 2008	USA	Liquidity risk (funding and market)	Spreads	DCC-GARCH (2006 : Capiello, Engle and Sheppard)	1/ Monte carlo. 2/Boostrap	funding illiquidity increased sharply during the subprime crisis and the bank solvency became important
		subprime crisis.										issue.

Table 4 : Descriptive statistics on the G14 CDS returns.

 4

	Whole period (January 14, 2004 -May 27, 2009)
		RBAR	RBNP	RBOA	RCG	RCS	RDB	RGS	RHSBC	RJPM	RMS	RSG	RRBS	RUBS	RWF
	Mean	0,94	0,69	0,80	1,08	0,64	0,63	0,57	0,68	0,57	0,76	0,76	0,97	0,90	0,67
	Median	-0,23	-0,13	-0,25	-0,04	-0,34	-0,24	0,00	-0,67	-0,39	-0,04	-0,43	-0,41	-0,23	0,00
	Maximum	62,40	59,64	47,05	73,24	67,47	69,58	117,13	61,87	46,94	111,26	61,74	84,75	90,69	58,72
	Minimum	-62,48	-36,15	-45,68	-81,06	-41,39	-47,93	-62,39	-31,18	-44,04	-96,06	-47,83	-85,82	-38,32	-63,53
	Std. Dev.	12,92	11,87	11,27	12,60	11,02	12,09	13,38	11,70	10,82	13,44	11,46	15,10	12,16	12,99
	Skewness	0,38	0,99	0,46	0,82	0,92	0,64	2,02	1,25	0,33	0,89	1,18	0,00	1,74	0,26
	Kurtosis	8,97	8,52	6,81	16,10	10,22	8,62	25,34	8,42	6,98	29,08	11,09	14,36	15,14	9,08
	Jarque-Bera	423,75	402,24	179,63	2041,20	650,38	389,17	6035,23	416,84	190,35	7999,05	831,93	1509,72	1867,70	436,50
	Observations	281	281	281	281	281	281	281	281	281	281	281	281	281	281
	Pre-crisis period (January 14, 2004 -September 10, 2008)
		RBAR	RBNP	RBOA	RCG	RCS	RDB	RGS	RHSBC	RJPM	RMS	RSG	RRBS	RUBS	RWF
	Mean	1,02	0,71	0,86	0,96	0,65	0,66	0,73	0,69	0,74	0,85	0,84	0,95	1,03	0,80
	Median	-0,21	-0,17	-0,52	-0,01	-0,34	-0,25	0,00	-0,63	-0,40	0,00	-0,41	-0,43	-0,18	0,00
	Maximum	62,40	59,64	47,05	69,87	47,44	42,18	51,93	61,87	42,07	44,25	61,74	84,75	51,63	54,92
	Minimum	-32,83	-32,90	-29,26	-24,31	-32,24	-32,47	-36,58	-27,76	-24,48	-41,67	-32,20	-85,82	-32,45	-29,93
	Std. Dev.	10,76	10,51	9,29	9,78	9,68	9,93	10,27	10,04	9,09	9,39	10,26	13,20	10,14	10,57
	Skewness	1,14	1,52	0,95	2,23	0,72	0,58	0,42	1,42	0,80	0,00	1,74	0,49	1,18	1,15
	Kurtosis	9,14	11,16	7,11	15,10	8,04	6,89	7,67	9,54	5,87	7,94	13,29	17,73	8,10	8,59
	Jarque-Bera	435,94	771,31	208,35	1691,52	279,41	167,31	228,80	516,27	110,15	248,09	1200,57	2216,00	320,95	371,96
	Observations	244	244	244	244	244	244	244	244	244	244	244	244	244	244
	Global Financial Crisis period (September 17, 2008 -May 27, 2009)
		RBAR	RBNP	RBOA	RCG	RCS	RDB	RGS	RHSBC	RJPM	RMS	RSG	RRBS	RUBS	RWF
	Mean	0,44	0,52	0,39	1,87	0,58	0,43	-0,46	0,58	-0,51	0,19	0,22	1,13	0,04	-0,15
	Median	-2,76	1,33	2,05	-2,27	1,92	0,76	-0,03	-0,73	-0,18	-1,30	-1,39	0,48	-1,11	-0,19
	Maximum	58,25	53,17	44,20	73,24	67,47	69,58	117,13	59,82	46,94	111,26	55,51	64,56	90,69	58,72
	Minimum

Table 5 : EGARCH models -Whole sample (January 14, 2004 -May 27, 2009).

 5 This table shows the results of the estimates of the conditional variance for each bank of the sample. We use EGARCH model to allow for asymmetric effect in the conditional variance. To estimate the conditional variance, we need 2 equations, the mean equation and the variance equation. The

	following equations are estimated for each univariate serie :	∑		and
	log	∑		∑	log	. This table shows also the results of
	the Q, Q^2 and ARCH test for 20 lags. *** denotes the significance level at 1%, ** denotes the
	significance level at 5%, * denotes the significance level at 10%. The values in parenthesis are the
	standard deviations. The value in [ ] are the P-value.
		MEAN	C	A	B	D	Q(20)	Q 2 (20)	ARCH(20)

Table 6 : DCC-GARCH model.

 6 These results are the estimation of the DCC-GARCH model for the 14 banks. The coefficient AFIX represents the effect of past shocks. The coefficient BFIX represents the effect of past covariance. And the coefficient of GFIX the effect of asymmetry. If the GFIX coefficient is significant, then means that a bad news would have a more negative effect on correlations than good news.

	The following equation

Table 7 : Results from the ADCC-AR regression.

 7 This table shows the coefficient of the dummy GFC from the AR regression. The following equation for Model 1 is tested For instance, the dynamic conditional correlation of Citigroup with Wells Fargo significantly increased by 0.93% during the global financial crisis. The results are presented for each banks of the sample. The coefficients for the correlation between Citigroup and Goldman Sachs are the same than the coefficients for the correlation between Goldman Sachs and Citigroup,etc. The following equation for Model 2 is tested :

, ∑ , . , ∑ , .

Table 8 : The significance of dummy crisis coefficient from the ADCC-AR regression.

 8 This table shows the results of the effect of the GFC on banks pair correlations. On this table only are represented the significance level of the estimated coefficient associated with the dummy crisis. ** denotes the significance level at 5%, * denotes the significance level at 10%. ns denotes insignificant parameters.

		CG GS JPM MS WF BOA BNP DB HSBC RBS SG	UBS BAR CS
	CG		ns	ns	ns	**	ns	ns	*	**	*	ns	**	*	ns
	GS	ns		ns	*	ns	**	**	*	**	**	**	**	**	**
	JPM	ns	ns		ns	*	ns	ns	ns	*	ns	ns	*	ns	ns
	MS	ns	*	ns		ns	***	**	**	**	**	**	**	**	**
	WF	**	ns	*	ns		**	ns	ns	ns	ns	ns	**	ns	ns
	BOA	ns	**	ns	**	**		**	**	**	**	*	**	**	ns
	BNP	ns	**	ns	**	ns	**		ns	ns	ns	ns	**	ns	ns
	DB	*	**	ns	**	ns	**	ns		ns	ns	ns	*	ns	ns
	HSBC **	**	*	**	ns	**	ns	ns		*	ns	*	ns	ns
	RBS	*	**	ns	**	ns	**	ns	ns	*		**	ns	*	ns
	SG	ns	**	ns	**	ns	*	ns	ns	ns	**		ns	ns	ns
	UBS	**	**	*	**	**	**	**	*	*	ns	ns		ns	*
	BAR	*	**	ns	**	ns	**	ns	ns	ns	*	ns	ns		ns
	CS	ns	**	ns	**	ns	ns	ns	ns	ns	ns	ns	*	ns

Table 9 : The dummy crisis coefficient from the ADCC-AR regression.

 9 This table shows the results of the effect of the GFC on banks pair correlations. The following equation is estimated (model 1) : , ∑ ** denotes the significance level at 1%, ** denotes the significance level at 5%, * denotes the significance level at 10%. The values in parenthesis are the standard deviations.

,

. On this table only are represented the estimated coefficient associated with the dummy crisis. *

Table 12 : Subprime writedowns and credit losses and capital raised in billions of dollars announced by the G14 banks from January 2007 to August 2008 (source: Bloomberg).

 12

	Financial Institutions Writedown & Loss Capital Raised
	Citigroup	55.1	49.1
	UBS	44.2	28.3
	HSBC	27.4	3.9
	Bank of America	21.2	20.7
	Royal Bank of Scotland	14.9	24.3
	Morgan Stanley	14.4	5.6
	JPMorgan Chase	14.3	7.9
	Deutsche Bank	10.8	3.2
	Credit Suisse	10.5	2.7
	Wells Fargo	10	4.1
	Barclays	9.1	18.6
	Societe Generale	6.8	9.8
	BNP Paribas	4	-
	Goldman Sachs	3.8	0.6

See table 1 for a description of the sample.

Basel

introduced the liquidity coverage ratio (LCR) for the short-term and the Net Stable Funding Ratio (NSFR) for the long-term.

The weekly returns are computed as: (CDS premium for bank i at t -CDS premium for bank I at t-1)/CDS premium for bank i at t-1)*100. Then we interpret positive CDS return as the CDS premium for bank i in t is superior to CDS premium for bank i in t-1, a sign of higher default risk for bank i. The bank i is considered by investors as more risky.

Citigroup

-0,47 1,121** 0,394*** 0,764*** -0,259** 27,093 28,870* 1,139 (0,292) (0,524) (0,089) (0,038) (0,105) [0,133] [0,050] [0,310] Goldman -0,193 3,259** 1,131*** 0,606*** -0,932*** 6,770 2,103 0,099 Sachs (0,344) (1,395) (0,303) (0,069) (0,282) [0,997] [0,100] [1,000] JP Morgan -0,148 3,210*** 0,328*** 0,777*** -0,270*** 25,441 20,968 0,945 (0,411) (1,101) (0,088) (0,053) (0,088) [0,185] [0,281] [0,531] Morgan -0,303 0,862* 0,460*** 0,830*** -0,415*** 14,633 1,360 0,064 Stanley (0,308) (0,453) (0,106) (0,022) (0,137) [0,797] [1,000] [1,000] Wells -0,170*** 34,663*** 0,278*** 0,626*** -0,340*** 19,628 11,516 0,520 Fargo (0,008) (0,51) (0,001) (0,001) (0,002) [0,481] [0,871] [0,957] Bank of 0,027 1,651** 0,199*** 0,846*** -0,085 14,870 16,340 0,732 America (0,43) (0,752) (0,06) (0,039) (0,076) [0,784] [0,569] [0,791] BNP -0,463 1,653** 0,380** 0,741*** -0,136 26,756 8,544 0,407 Paribas (0,319) (0,631) (0,149) (0,054) (0,193) [0,142] [0,969] [0,990] Deutsche -0,605** 1,079* 0,379*** 0,659*** 0,25 19,880 6,139 0,302 Bank (0,294) (0,634) (0,109) (0,064) (0,188) [0,465] [0,996] [0,999] HSBC 0,225 1,140*** 0,107*** 0,952*** -0,177*** 30,588* 13,836* 1,361 (0,418) (-0,286) (0,017) (0,014) (0,036) [0,061] [0,086] [0,199] RBS 0,83 51,438** 0,430** 0,529*** -0,435** 25,193 2,639 0,105 (0,683) (16,141) (0,167) (0,129) (0,176) [0,194] [0,999] [1,000] Société -0,292 1,647** 0,440** 0,725*** -0,239 22,534 6,759 0,268 Générale (0,29) (0,595) (0,168) (0,061) (-0,188) [0,312] [0,992] [0,999] UBS -0,738** 1,530* 1,193** 0,583*** -0,778** 16,844 6,597 0,276 (0,297) (0,795) (0,403) (0,082) (0,352) [0,663] [0,993] [0,999] Barclays 0,138 3,023** 0,241** 0,868*** -0,302*** 26,176 13,869 0,649 (0,408) (1,099) (0,076) (0,042) (0,08) [0,160] [0,738]

Appendix

Schema 1: Risks during the subprime crisis. Source: Author.

Interest rate risk

Asset prices' collapse on real estate market (bursting of a bubble)

Rising delinquency rates on subprime loans

Dooley and Hutchison (2009)

Analysis of the spillover effect of the US subprime crisis on sovereign CDS spreads of emerging markets.