Analysis of European sovereign CDS spreads before and after the financial crisis

Analysis of European sovereign CDS spreads before and after the financial crisis Dorthe A. Winckelmann Lasse K. Sørensen MSc Finance Thesis Supervisor: Peter Løchte Jørgensen Department of Business Studies Aarhus School of Business, University of Aarhus August 2011

c Dorthe A. Winckelmann & Lasse K. Sørensen 2011 The thesis has been typed with Computer Modern 11pt Layout and typography is made by the authors using L A TEX We would like to thank our supervisor Peter Løchte Jørgensen for help along the way. The good people of the library who ensured that the last semester was not only thesis writing are very much appreciated.

Abstract This thesis has investigated the determinants of sovereign CDS spreads before and after the financial crisis for 11 European countries. The period of analysis is January 2006 to April 2011, which has been divided into 3 sub periods. The first period is the time up until the default of Lehman Brothers in September 2008. The second period lasts until late 2009 and is marked by the implementation of bank rescue packages and a subsequent financial stabilization. The third period is characterized by the European debt crisis. Since June 2007 the sovereign CDS market has attracted considerable attention and the credit markets have been subject to an unprecedented repricing of credit risk. The collapse of Lehman Brothers resulted in large losses for many financial entities which caused damaged investor confidence and a decline in the availability of credit. Massive support for the banks and other stimuli increased the public sector deficits and took the sovereign debt to record high levels. This meant that the risk of default of developed sovereigns became real especially for a number of European countries. The first part of the analysis examines the risk transfers between the banks and the sovereigns. The results indicate that a risk transfer from the banks to the sovereigns took place in October 2008 with the introduction of financial rescue packages. However, the development of the sovereign debt levels and the pressure on the European economy induced that some of this risk was transferred back to the banks from November 2009. The next step in the analysis shows a strong co movement across the countries in both CDS and bond spreads. The nature of this co movement is examined by OLS regression and is for CDS spreads found to be very similar to the itraxx Europe index. For bond spreads none of the chosen market factors were able to explain the co movement. For the actual analysis of the determinants a number of theoretical determinants are identified based on the Black Scholes Merton structural framework and previous research. This results in three groups of variables; global, local and risk. The overall findings indicate that in period 1 global factors are dominating, both for CDS and bond spreads. In period 2 and 3 the local variables gain more explanatory power. Moreover in period 3 the risk factors become significant. Hence, a repricing of sovereign risk has taken place. Finally an examination of the price discovery in the CDS and bond market, using Granger s causality test, shows that the CDSs have gained more significance in the pricing process through the three periods.

Contents Contents List of Figures List of Tables i iii iv 1 Introduction 1 1.1 Problem statement................................ 3 1.1.1 Data description............................. 4 1.1.2 Delimitations............................... 5 2 Credit default swaps 7 2.1 Credit default swaps............................... 7 2.1.1 The use of CDSs............................. 8 2.2 Pricing....................................... 10 2.2.1 Static replication............................. 11 2.2.2 Modeling................................. 12 2.2.3 Empirical use of models......................... 18 3 The European Economy 19 3.1 Developments on the macro-level........................ 19 3.1.1 Fiscal Policy............................... 21 3.1.2 Debt and Interest Rates......................... 23 3.2 Financial Institutions............................... 29 3.2.1 The case of Ireland............................ 32 3.2.2 The sovereign debt crisis......................... 32 3.3 Risk transfer................................... 35 3.3.1 Examination method........................... 36 3.3.2 Results.................................. 37 i

Contents 4 Assessment of the regression assumptions 40 4.1 Gauss Markov assumptions........................... 40 4.1.1 Endogeniety................................ 40 4.1.2 Heteroskedasticity and auto correlation................ 41 4.1.3 Normal distribution of the residuals.................. 42 4.1.4 Stationarity................................ 42 4.1.5 Multicollinearity and significance level................. 43 5 Principal Component Analysis 44 5.1 PCA results.................................... 45 5.2 Analyzing the common factors......................... 48 5.2.1 CDS.................................... 49 5.2.2 Bonds................................... 52 6 Determinants of CDS and bond spreads 54 6.1 Theoretical determinants............................. 54 6.1.1 Global factors............................... 55 6.1.2 Local factors............................... 60 6.1.3 Risk factors................................ 65 6.2 Regression results................................. 66 6.2.1 Discussion of regression assumptions.................. 67 6.2.2 CDS spreads............................... 68 6.2.3 Bond spreads............................... 82 6.2.4 CDS vs. Bonds.............................. 88 6.2.5 Robustness................................ 91 6.3 Lead-lag analysis................................. 92 6.3.1 Granger s causality test......................... 92 6.3.2 Results.................................. 93 7 Reflections 95 8 Conclusion 97 Bibliography 100 A Appendix 105 ii

List of Figures 2.1 CDS payment obligations.............................. 7 3.1 European Sovereign CDS Spreads.......................... 19 3.2 Notional amount of outstanding CDS........................ 21 3.3 Government bond spread to the 2 and 10 year euro swap rate......... 23 3.4 Debt/GDP ratio................................... 24 3.5 10 Year Spreads (government bond euroswap rate)............... 25 3.6 Bank CDS spreads April 2007 to October 2008.................. 30 3.7 Bank CDS spreads September 2008 to November 2009.............. 31 3.8 Sovereign and bank CDS of Ireland......................... 32 3.9 Bank CDS spreads November 2009 to March 2011................ 34 3.10 Relation between itraxx and CDS spreads Portugal.............. 38 5.1 Loadings for PC1................................... 48 A.1 Relation between itraxx and CDS spreads Denmark.............. 115 A.2 Relation between itraxx and CDS spreads Germany.............. 115 A.3 Relation between itraxx and CDS spreads France............... 115 A.4 Relation between itraxx and CDS spreads Greece............... 116 A.5 Relation between itraxx and CDS spreads Ireland............... 116 A.6 Relation between itraxx and CDS spreads Italy................. 116 A.7 Relation between itraxx and CDS spreads Sweden............... 117 A.8 Relation between itraxx and CDS spreads UK................. 117 A.9 Relation between itraxx and CDS spreads Spain................ 117 iii

List of Tables 3.1 Public budget balance as a percentage of GDP.................. 22 3.2 Exposure by European Banks to the GISP countries............... 33 5.1 Cumulative proportion explained by principal component (in %)........ 45 5.2 CDS spreads - Correlation matrix.......................... 46 5.3 Regression of the first principal component - CDS................. 50 5.4 Regression of the first principal component - bonds................ 53 6.1 Expected sign of variables.............................. 66 6.2 CDS 10 year Period 1............................... 69 6.3 CDS 10 year Period 2............................... 72 6.4 CDS 10 year Period 3............................... 76 6.5 Bonds 10 year Period 1.............................. 82 6.6 Bonds 10 year Period 2.............................. 84 6.7 Bonds 10 year Period 3.............................. 85 6.8 Correlations between CDS and bond spreads in first differences......... 89 6.9 Lead-lag relationship between CDS and bond spreads.............. 94 A.1 CDS 10 year whole period.............................. 111 A.2 CDS 10 year 3 periods............................... 111 A.3 CDS 5 year whole period.............................. 111 A.4 Bonds 10 year whole period............................. 112 A.5 Bonds 10 year 3 periods.............................. 112 A.6 Bonds 5 year whole period............................. 112 A.7 Regression of itraxx on sovereign CDS spreads - Levels............. 113 A.8 Regression of itraxx on bank CDS spreads - Levels................ 113 A.9 Regression of itraxx on sovereign CDS spreads - First differences........ 114 iv

List of Tables A.10 Regression of itraxx on bank CDS spreads - First differences.......... 114 A.11 Cumulative proportion explained by principal component (in %)........ 118 A.12 10 year PC1 regressions results - CDS all period 1................ 119 A.13 10 year PC1 regressions results - CDS all period 2................ 119 A.14 10 year PC1 regressions results - CDS all period 3................ 119 A.15 10 year PC1 regressions results - CDS selected period 1............. 120 A.16 10 year PC1 regression results - CDS selected period 2............. 120 A.17 10 year PC1 regressions results - CDS selected period 3............. 120 A.18 5 year PC1 regressions results - CDS all..................... 121 A.19 5 year PC1 regressions results - CDS selected.................. 121 A.20 10 year PC1 regressions results - bonds period 1................. 122 A.21 10 year PC1 regressions results - bonds period 2................. 122 A.22 10 year PC1 regressions results - bonds period 3................. 122 A.23 5 year PC1 regression results - bonds........................ 123 A.24 CDS 5 year Period 1................................ 124 A.25 CDS 5 year Period 2................................ 124 A.26 CDS 5 year Period 3................................ 125 A.27 Bonds 5 year Period 1............................... 125 A.28 Bonds 5 year Period 2............................... 126 A.29 Bonds 5 year Period 3............................... 126 A.30 CDS Jarque Bera and F test statistics...................... 127 A.31 Bonds Jarque Bera and F test statistics..................... 127 v

1 Introduction Since June 2007 the sovereign credit default swap (CDS) market has attracted considerable attention and the credit markets have been subject to an unprecedented repricing of credit risk. Before the financial crisis trading in the sovereign credit market was less profound compared to trading in the corporate credit risk market and the liquidity in the sovereign CDS market was low as a result of the financial markets assessment of the minimal default risk of developed countries. However, the collapse of Lehman Brothers resulted in large losses for many financial entities which caused damaged investor confidence and a decline in the availability of credit. Massive financial support for the banks and other stimuli increased the public sector deficits. This took the sovereign debt to record high levels and the risk of default of developed sovereigns became real. These events caused a reassessment of the credit risk of developed countries and led to an increase in the trading of CDSs implying a higher liquidity of sovereign credit risk. CDSs on sovereign debt serve as an insurance instrument which transfers the risk of default from the buyer to the seller. The price of CDSs does however also serve other purposes and is now also a market indicator widely used by the financial markets. Due to the escalating European sovereign debt crisis, many politicians accused the use of CDSs of exacerbating the financial crisis (Oakley, Tett and Hughes, 2010). The absence of default of developed sovereigns have caused a general perception that government bonds have been a good proxy for the risk free rate (Fontana and Scheicher, 2010). For this reason former research have focused more on CDSs on emerging market debt and the inherent default risk of emerging economies. For developed economies the focus has been on CDSs on corporate debt and determinants of government bond yields. CDSs are a fairly new instrument and as earlier mentioned the liquidity in sovereign CDS spreads was low prior to the financial crisis. This has resulted in more research on government bond yields as opposed to CDSs. Therefore, the increasing focus on CDSs and on the debt of developed economies along 1

with the turbulent financial situation in the European Union (EU) inspired the authors of the thesis to investigate the drivers of the price of default insurance of 11 European countries. Five of these countries are the so called GIISP countries consisting of Greece, Ireland, Italy, Spain and Portugal which are all characterized by high debt levels which have attracted significant amount of attention from the markets and the media. Of the remaining six countries three are euro countries (Finland, Germany and France) and three countries are outside the European Monetary Union (Denmark, UK and Sweden). The purpose of including countries with different characteristics is to enable a deeper and more diversified analysis. Motivated by the above development, this thesis will focus on the analysis of the determinants of sovereign CDS spreads as well as sovereign bond spreads. Sovereign CDSs are derivatives written on government bonds hence the analysis enables a comparison of the two sets of drivers. Furthermore, the spreads are analyzed in light of the financial crisis and the ongoing sovereign debt crisis by investigating the period January 2006 to April 2011. The five year period is split into three sub periods in order to compare information between these three distinct periods. The analysis of the determinants is based on a discussion of the theoretical approach of credit risk and an examination of the financial situation in Europe. The latter part includes a section on the risk transfer between the financial sector and the governments. This part is inspired by and Ejsing and Lemke (2010) and should be seen in relation to the major bank rescue packages provided to the financial system. The same researchers have also documented that a single common factor accounts for a high degree of the variation in the CDS and bond spreads. Hence, before analyzing the determinants of the spreads, the common factors of the spreads of the eleven countries are analyzed and regressed upon several global market factors in order to identify the nature of the common factor. Along with these global factors, a set of local and risk factors are regressed upon the CDS and bond spreads to identify the determinants of spreads. The last part of the analysis is inspired by Fontana and Scheicher (2010) and examines whether it is the CDS spreads or the bond spreads that play a dominating role in price discovery in the two markets. Since CDS spreads are the price of credit risk, identifying the determinants of CDS spreads enables an understanding of which risk factors are related to entering a CDS contract. At the same time, a deeper understanding of the drivers of CDS spreads allows the financial markets, which use the CDS spreads as an indicator, to assess the effect of changes in global or local factors on the price of credit risk. 2

1.1. Problem statement 1.1 Problem statement The main purpose of the thesis is to analyze sovereign credit default swap spreads of 11 European countries before, during and after the financial crisis In addressing the main purpose, the analysis is centered around three main points. The main focus is to identify the determinants of CDS and bond spreads, comparing the results across periods to see whether the determinants have changed due to the financial crisis 1 and comparing the CDSs and bonds findings. Furthermore the price discovery in the CDS and bond market is examined. Also the risk transfer between the financial sector and the public sector reflected by sovereign and financial institutions CDS spreads is analyzed. The thesis is structured in a number of sections which contributes to the main purpose. Section 2 presents an overview of CDSs and their use in the financial world. Furthermore this section describes the pricing process of CDSs by presenting the theoretical modeling of credit spreads and identifying possible theoretical determinants. Furthermore the empirical use of these models is discussed. Section 3 outlines the development of the European economy focusing on the 11 countries on a macro-level. After this follows a description of the situation of the European financial sector and the impact of the sovereign debt crisis. Furthermore this section analyzes the possible risk transfers between the financial sectors and the sovereigns. Section 4 provides an overview of the statistical properties of ordinary least squares (OLS) and the Gauss Markow assumptions along with the approach to deal with possible violations of the assumptions. Section 5 contains a principal component analysis of the CDS and bond spreads to identify the sources of communality in the spreads movements during the sample period conducted using Eviews. Afterwards the first common factor is regressed upon several market factors, using OLS regression in Eviews, to determine the nature of the first common factor. Section 6 presents the theoretical determinants of CDS and bond spreads. Furthermore 1 The beginning of the financial crisis is defined as mid September 2008 - following the fall of Lehman Brothers 3

1.1. Problem statement extensive regression analysis (OLS) of the spreads is conducted in Eviews to identify which factors have an influence on the development of these spreads and how they have changed during the sample period. Finally a lead-lag analysis of CDS and bond spreads is conducted to find out in which market the pricing takes place using Granger s causality test in Eviews. Section 7 and 8 finishes the thesis with a reflection on the results and a general conclusion. 1.1.1 Data description The thesis examines CDS spreads on 11 EU-countries; 3 countries outside the euro: UK, Denmark and Sweden and 8 euro countries: Ireland, Greece, Portugal, Spain, Italy, Germany, France and Finland. The selection of countries is based on data availability and with the aim of creating a representative picture of the EU area countries by including countries perceived both as healthy and non-healthy. The data consists of 5- and 10-year single name dollar-denominated CDS spreads quoted as mid-prices. 2 5- and 10-year spreads are chosen since they are the most liquid maturities (Pan and Singleton, 2008; Dieckmann and Plank, 2011; Benkert, 2004). The observations used are weekly and obtained from Bloomberg and Datastream. The sample period covers 01.01.2006-18.03.2011. This period is chosen to cover the period before, during and after the financial crisis. All data is split into three sub periods based on the spreads development, see figure 3.1. Period 1 is defined as 01.01.2006-15.09.2008, period 2 as 16.09.2009-31.10.2009 and period 3 as 01.11.2009-18.03.2011. Bond spreads are calculated relative to the Euro swap-rate since this is considered as the markets participants preferred measure of the risk free rate due to its high liquidity and relatively low counterparty risk (Fontana and Scheicher, 2010; Beber, Brandt and Kavajecz, 2009). At the same time the Euro-swap rate is considered a homogeneous benchmark across the Euro-area. Some studies apply the German government bond rate but since this would exclude Germany from the analysis, this method has been deselected. Both the bond yields and the Euro swap-rate are obtained through Nordea Analytics and have the same maturity as the CDS spreads. For the analysis of risk transfer between banks and sovereigns the set of banks used by 2 Mid-price is the average of the bid and ask price 4

1.1. Problem statement Ejsing and Lemke (2010) is used as a basis for the selection of banks for this thesis. However, no CDSs for Finnish banks are included due to data availability. When analyzing the determinants of the CDS and bond spreads it is necessary to convert the different data into the same weekly time-interval as the CDS spreads. To do this we apply the cubic spline function named spline(), from Matlab. One example is Debt/GDP where the data is obtained in yearly intervals. To have the most accurate interpolation, the first data-point is 2005 under the assumption that the yearly values are ending-year-values, thus the year 2005 value is a good indicator of the beginning-yearvalue of 2006. Applying the interpolated data in the regression analyses introduces the problem of autocorrelation because the data points are related to each other by a cubic polynomial and hence violate the standard OLS assumption of no autocorrelation. Therefore Newey-West standard errors are used since they are robust to autocorrelation. Excel spreadsheets containing the data used for regression, stationarity check and correlation overview are attached to the thesis. 1.1.2 Delimitations This thesis main focus is on CDS spreads as opposed to bond spreads. One advantage of CDS spreads is that they are already spreads which means that there is no noise from misspecified model of risk-free yield curve (Ericsson, Jacobs and Oviedo, 2009). Also some researchers have found that CDSs reflect changes in credit risk more accurately and quickly than bond spreads, e.g. Blanco, Brennan and Marsh (2005). As opposed to bonds, CDSs are designed so that there is no cash flow at initiation of the contract which makes them easier to enter compared to bonds. Issue size and liquidity are also factors that do not need to be taken into account when working with CDSs (Bomfim, 2005). Due to the ongoing financial turbulence in the EU it has been necessary to define an end date of the data period. This point in time is April 2011. Throughout the thesis the statistical analyses are made on both 5 & 10 year dollar denominated CDS and bond spreads. Only the results for 10-year spreads are reported in the thesis while 5-year spreads are used as a robustness check. The applied data is primarily from Bloomberg while Datastream is used as a supplement. 5

1.1. Problem statement Using data from two different sources can cause deviations in data. If data is missing for some countries for specific dates, e.g. bank holidays, the previous week s observation is used. This thesis will not focus on counterparty risk in CDS contracts. Counterparty risk has become a more important factor in the pricing of CDS contracts after the financial crisis, in which banks were actually able to default and many CDS contracts had banks as counterparts. If the counterpart defaults it means that the value of the insurance to the buyer is zero. Hence, a higher counterparty risk would have a decreasing effect on the spread paid to the seller of the CDS. Quantifying this risk is however very complicated and would serve as a thesis topic in itself. No political factors are included in the possible determinants of CDS spreads since these kind of factors can be very hard to quantify and the data available is sparse. 6

2 Credit default swaps 2.1 Credit default swaps Credit risk is defined as the risk that an obligor does not honour his payments due to a default event (Bomfim, 2005). Credit default swaps were introduced in the mid 90 s and quickly became a popular OTC derivative. CDSs represent the cost of assuming pure credit risk as opposed to for example a bond which represents several risks such as interest rate, foreign exchange and credit risk. Before CDSs were available a bond investor s way to adjust credit risk was to buy or sell the bond which would effect the investor s position on all risks. CDSs provide the ability for investors to independently manage the credit risk (Beinstein and Scott, 2006). Figure 2.1 shows the change of cash flows in a standard CDS agreement. A CDS can be seen as an insurance that transfers the default risk of a certain individual entity, such as a company or a sovereign, from the protection buyer to the protection seller in exchange for the payment of a fee, also called the spread. The spread generally remains constant until the contract matures. One exception Figure 2.1: CDS payment obligations Spread Protection buyer No credit event: No payment Credit event: Payment Protection Protection seller Reference entity Source: Weistroffer (2009) though is the constant maturity CDS for which the credit spread is reset periodically to the current market level (Weistroffer, 2009). In case of default of the reference entity, the protection buyer receives compensation from the protection seller. The settlement method is determined upfront when the contract is entered and can be done either by 7

2.1. Credit default swaps physical or cash settlement. The former means paying the face value of the bond in exchange for the defaulted bond and the latter means paying the difference between the post-default market value of the bond and the par value. The post-default value is fixed by an auction procedure (Bomfim, 2005). The spread is the insurance premium that is paid for protection against default and is quoted in basis points (bps) per year as a fraction of the underlying notional. The notional amount represents the amount of insurance coverage. As with a standard interest rate swap the premium is set so that the CDS contract has a value of zero at initiation. A standard CDS contract written on corporate or public debt terminates either at the stated maturity or if one of the following credit events occurs. These protection triggering events are defined by the International Swaps and Derivatives Association (ISDA) and are 1 Bankruptcy (only relevant for corporate entities) Failure to pay coupons on bonds Debt moratorium (delay of payment of debt) or debt repudiation (rejection of debt) Restructuring of debt (Reduction and renegotiation of delinquent debt in order to improve or restore liquidity. Not always considered as default, e.g. in 2009 US contracts eliminated restructuring as a potential trigger event) Acceleration (lender forces the debt to terminate because of violation of the debt clauses by the borrower, e.g. downgrade of credit rating) Another important implication of CDSs is the confidentiality of transactions. The reference entity whose credit risk is being transferred is not a part of the transaction and therefore not aware of it. This means risk managers are able to transfer credit risk discreetly without effecting any business relationships (Beinstein and Scott, 2006). 2.1.1 The use of CDSs Sovereign CDS contracts are like most CDS contracts used as trading instruments rather than pure insurance. At the most basic level CDSs are, from a buyer s point of view used to buy default insurance and from the seller s used as an additional source of income. The CDSs are however in practice used by the market participants for several other purposes than this. 1 Weistroffer (2009) 8

2.1. Credit default swaps Many banks have large holdings of government bonds and with the development seen in the European countries, banks can use sovereign CDS to hedge their country risk. This development will be further discussed in section 3.2. Banks also use CDSs to export risk from their balance sheets which results in a lower required capital reserve due to regulation. The CDS market enables banks to go short in credit and in this way transform buckets of risk using derivatives and thus undermine the fundamental idea of capital weights implemented with the Basel requirements. This is favourable since the banks transform risk without trading as much in the underlying (Blundell-Wignall and Atkinson, 2010). Furthermore, some market participants also enter CDS contracts even if they do not have any exposure to the underlying, also called a naked position. This makes buying the CDS similar to shorting the underlying bond since the market value of the position in the CDS would increase as the credit quality of the reference entity deteriorates. During the financial crisis banks and hedge funds have been accused of exacerbating the crisis using naked positions (Delatte, Gex and Villavicencio, 2010). Sellers of CDSs use the market to enhance yields on their portfolios and to diversify their credit risk exposure i.e. tailoring their credit risk profile. One thing that is especially motivating for protection sellers is the fact that entering a CDS contract does not require any upfront funding and the seller can thereby obtain exposure to large amounts of debt with essentially no upfront cost - except for the possible cost of posting collateral (to minimize counterparty risk, seen from the buyers perspective). This can be especially attractive to investors with high funding cost. This is opposed to getting the same exposure by buying the bonds issued by the reference entity which would require a significant initial cash outlay. Furthermore CDSs are attractive since they enable investors to obtain exposure to entities which would otherwise be difficult to establish, e.g. a company whose debt is closely held by a small number of investors. Instead an investor can sell a CDS contract and in this way receive a cash flow which is closely linked to the cash flow that investors would have received from buying the reference entity s debt directly, also called a synthetic position (Bomfim, 2005). CDSs can also be used for arbitrage trading, e.g. government bonds vs. CDSs, also called basis arbitrage. The basis is defined as the difference between the CDS spread and the spread on the underlying government bond. The basis provides insight to how well sovereign credit markets function because the CDSs and underlying bonds tend to trade similarly due to the market s view on default risk (Beinstein and Scott, 2006; Fontana and Scheicher, 2010). Hence, both sovereign bonds and CDSs offer exposure to sovereign debt. Taking the example of Greece, the increasing risk of a restructuring of 9

2.2. Pricing the Greek debt is reflected in at the same time increasing CDS spreads and increasing interest rates on government bonds. The value of the basis should be close to zero due to arbitrage trading because if the basis is either negative or positive then market participants may benefit from trading in both the bond and CDS market enabling them to lock-in a certain return. A positive basis, meaning that the CDS spread is higher than the bond spread, is observed for most sovereigns whereas a negative basis is observed for most corporations. To exploit a negative basis the investors should set up a default-risk free position by buying the underlying bond and buying protection through the CDS. To benefit from a positive basis the investor short-sells the bond and sells protection (Fontana and Scheicher, 2010; Beinstein and Scott, 2006). Another important use of CDSs is the use as a market indicator as CDS is a measure of the credit risk of an entity. CDSs are increasingly being used as an indicator of credit risk on the same level as yield spreads (e.g. Greek government bond rate vs. German bond rate or Euroswap). Bomfim (2005) suggests that CDS prices have a tendency to incorporate information more quickly than prices in the bond markets given that it at times might be easier to enter into a CDS contract than to buy/sell a certain bond. Whether the pricing takes place in the CDS market or the bond market will be analyzed in section 6.3. The value of a credit derivative can be determined by various methods which can largely be grouped in to two groups; static replication and modeling. 2.2 Pricing Main factors when pricing credit derivatives are the risks faced by the parties entering the contract. The seller is exposed to the risk that the reference entity will default during the duration of the contract and the seller will therefore have to cover the CDS buyer s loss. The buyer is exposed to the risk that the protection seller will not be able to cover the loss in the case of a credit event. This is also called counterparty risk. Also, the default correlation between the reference entity and the protection seller is important to the buyer since a scenario where both the reference entity and the seller default at the same time means the greatest loss for the buyer. The expected recovery rate is also an important factor since the payoff of a CDS contract, in case of default, depends on the post-default value of the reference entity s debt. The lower the default value the higher the price of 10

2.2. Pricing protection. Legal risk and model risk should also be taken into consideration. In the recent years, legal risk has though been reduced significantly with the development of the market (Bomfim, 2005). Different models and their empirical use will be discussed later in this section. In practice other factors than the fundamentals of the reference entity and the counterparty have influence the pricing of credit derivatives. This can for example be liquidity risk which arises due to the difference in the liquidity in the bond market and the CDS market. Using a portfolio replication method will miss the liquidity difference between the two markets. Furthermore, replication methods often use short selling which can be more difficult in the real world. Instead many investors use repurchase agreements which have additional costs. These factors mean that the market prices may deviate from the prices implied by the use of theoretical pricing methods. Large differences between these should however not be persisting since arbitrageurs and new market participants will have a reducing effect (Bomfim, 2005). 2.2.1 Static replication 2.2.1.1 The buyer The buyer s position is identical to short selling the underlying defaultable bond and investing the proceeds in a par default free floating rate note. This means that the investor will pay coupons on the short position of the risk free rate plus a spread, R f +S, depending on the credit quality of the issuer. At the same time the investor will receive coupons on the default free floating rate note, R f. The net payment will therefore be (R f + S)+R f = S (2.1) As earlier mentioned, in the real world it is not possible for most investors to short sell the underlying bond. Instead this is normally done by a repurchase agreement (repo) where the investor gives a collateralized loan to a person holding the bond and thereby obtains the bond. Hereafter the bond can be sold (shorted). At maturity (or default) the investor has to buy back the bond in the market and deliver the bond to the initial bond holder and in return receives the notional of the loan plus interest rates, R. In cases where the particular bond is hard to obtain as collateral, also called repo special, the associated repo rate may be below the typical rate, which will raise the cost of shorting (Duffie and Singleton, 2003). The repo rate received will in this case be R Z, where Z is the difference between the general rate and the specific rate for the repo special. The investor has to pay 11

2.2. Pricing coupons of R + S on the short position. This in total gives a net payment of (R Z) (R + S) = S Z (2.2) i.e. the protection buyer has to pay a spread of S + Z to the protection seller. 2.2.1.2 The seller From the protection seller s view the position is identical to going long in the underlying bond and shorting one risk free floating rate government bond. This will mean that the seller will receive R f + S from the long position and pay R f, which means that the seller will receive S. 2 However, In some cases it is not possible to find a replicating portfolio, e.g. illiquid markets where the bid-ask spreads are high instead modeling can be used. in very 2.2.2 Modeling The application of any model of default risk to CDSs is complicated since the traditional models are usually mainly concerned with pricing risky debt as opposed to valuing a credit derivative like a CDS. As argued earlier there is a close connection between bond spreads and CDS spreads which could justify the use of similar models and methods, but it has to be taken into consideration that there are differences between these two (Benkert, 2004). The existing literature on default risk modeling has presented two different approaches; structural models (also called firm value models) and reduced-form models. There are two important elements in default risk. First is the probability that the the reference entity defaults and secondly the size of the loss that the bond holders suffer in case of default. 2.2.2.1 Structural models Structural models focus on the analysis of capital structure and was initially laid out by Black and Scholes in 1973 and Merton in 1974 (Duffie and Singleton, 2003). The Black- Scholes-Merton (BSM) framework was oriented towards analyzing corporate credit risk, and Gapen, Gray, Lim and Xiao (2005) extended this framework to sovereign credit risk. Gapen et al. (2005) identified that key credit risk indicators of sovereign default are the 2 As also mentioned above it is not normally possible for e.g. a company to be able to short sell a government bond, instead the company has to enter a repo agreement, which can have cost of Z. The payout from the position will therefore be R f + S R f Z = S Z. 12

2.2. Pricing volatility of sovereign assets and a country s leverage. The basic framework for pricing sovereign CDSs is however overall identical to the framework used for corporate CDSs (Pan and Singleton, 2008). The BSM framework considers a firm with a very simple capital structure consisting of one zero coupon bond with a face value of K and maturity T and one equity share, E. The assumption of one bond and one share is not restrictive and more generally the K can be thought of as the total value of the firm s debt where all debt is zero coupon bonds maturing at time T and E is the total value of the shares issued by the firm. The market value of the firm s assets, A(t), can be expressed as A(t) =E(t)+Z d (t, T )K (2.3) where Z d (t, T ) is the discount factor for the firm s debt. Application of this model to sovereigns poses the problem that sovereigns are not assigned an entity value. Instead for example GDP growth can be used as a determinant of debt capacity (Ericsson et al., 2009). The BSM model assumes that default can only occur at maturity T and will occur only if the value of the firm s assets is below the face value of the debt. This would mean that the firm is worth less than the debt to the bond holders. If the company defaults, the shareholders receive nothing and the debt holders receive A(t), i.e. the recovery value = A(t). If the firm does not default the bond holders will receive K. If Z d (T,T)K is the amount that the debt holders will receive at time T, the bond holders payout can be expressed as Z d (T,T)K = K Max(K A(T ), 0) (2.4) Which at time t prices is Z d (t, T )K = e R(t,T )(T t) K p(t, A(t); T,K) (2.5) The shareholders can either receive A(T)-K or nothing at time T and their pay off can be expressed as E(T )=Max(A(T ) K), 0) (2.6) Looking closer at these payouts it can be seen the last element in equation 2.4 resembles that of a put option written on the firm s assets with a strike price of K. This put option however appears with a negative sign in equation 2.4 which means that the bond holder would have a position similar to being short in the put. In total the bond holders position is equivalent to being long in a risk-less zero coupon bond with face value K and a short position in the put option. From equation 2.6 it can be seen that the shareholder s payout 13

2.2. Pricing is similar to the payoff from a call option written on A with a strike of K. However, using the put-call parity 3 equation 2.6 can be rewritten to E(T )=A(T ) K + Max(K A(T ), 0) (2.7) which shows that the shareholder s position is equivalent to a portfolio including a long position in a put option - a put option which is implicitly bought from the debt holders (Bomfim, 2005). Equation 2.5 shows that the higher the value of the put option the larger the difference between the price of the defaultable bond and the risk free bond - which also means a wider credit spread. The Black-Scholes-Merton credit spread is defined as S(t, T )=Y (t, T ) R(t, T ) (2.8) where Y (t, T ) is the yield to maturity on the defaultable zero coupon bond and R(t, T ) is the rate on a risk-less zero coupon bond. The yield to maturity is found by isolating Y (t, T ) in Inserting this in equation 2.8 S(t, T )= Z d Y (t,t )(T t) (t, T )=e Y (t, T )= 1 (T t) ln 1 Z d (t, T ) 1 (T t) ln 1 Z d (t, T ) R(t, T ) (2.9) A higher value of the put means a higher probability of exercise which in this connection means that the firm is more likely to default. According to the BSM-model, issuers (who are also the shareholders) of defaultable bonds have to pay higher rates than on otherwise comparable risk less bonds because the issuers are implicitly buying a put option on the value of the firm - and the higher the value of this option, the lower is the credit quality of the firm (Bomfim, 2005). Mathematically it can be shown that the value of the put is increasing with the spread. This is done by inserting equation 2.5 in equation 2.9 for the credit spread, isolating for 3 C(t) P (t) =S(t) K B(t, T ) 14

2.2. Pricing the put and finally differentiating w.r.t. the spread S(t, T ) 4 dp ds(t, T ) =(T t)e (S(t,T )+R(t,T ))(T t) > 0 (2.10) For the put to be increasing in the spread the derivative of the put has to be larger than zero. Looking at equation 2.10 (T t) will always be positive since t < T and since the exponential function by definition returns a positive number the derivative will always be larger than zero. Furthermore, using that the put is increasing in the spread it can also be shown that the spread is increasing in the leverage ratio, which is defined as l(t) = e R(T,t)(T t) K A(t) (2.11) This is done by differentiating a rewrite of equation 2.9 w.r.t. the leverage ratio 5 ds(t, T ) dl(t) = 1 (T t) Φ( d 1 ) Φ( d 1 )l(t)+φ(d 2 )l(t) 2 > 0 (2.12) The intuition behind the derivative being larger than zero is again that t<t,thatthe standard normal distributions, Φ, by definition always returns a positive number and that the leverage ratio cannot be negative. That a higher leverage ratio results in a higher spread has economic intuition and this is relevant for identifying the determinants of the CDS spreads. 2.2.2.2 Credit default swap valuation Pricing a CDS can be done using the BSM framework and extending it to a first-passage model, which allows for default before time T. It is assumed that the value of the firm is observable and given by the SDE da(t) A(t) = rdt + σdz(t) (2.13) where Z denotes a standard Brownian motion, σ is the volatility and r is the constant risk free interest rate. When modeling a standard CDS an important starting point is that the 4 The full derivations are shown in appendix A.1 5 The full derivations are shown in appendix A.2 15

2.2. Pricing value at inception is zero and therefore the CDS premium is set so that the PV(Feeleg)=PV(Contingent leg) (2.14) where the fee leg is seen from the protection seller s point of view and is the expected annual payments discounted by the probability of credit survival. The contingent leg is seen from the protection buyer and is the expected contingent payment (notional-recovery rate) discounted by the probability of default (Beinstein and Scott, 2006). framework the spread can be modeled as Using this S (1 R) T t Z(t, v)e h(v t) hdv Z(t, v)e h(v,t) dv T t =(1 R)h (2.15) where R is the recovery rate and h is the annualized probability of default (Bomfim, 2005). For the full derivation see appendix A.3. The structural model implies that the main determinants of the likelihood and severity of default are financial leverage, volatility and the term structure of the risk free rate (Ericsson et al., 2009). The determinants of sovereign default can however differ from the ones of corporate default. Sovereign default is often a political decision which is influenced by factors such as balance of payment and central bank reserves. A sovereign rarely makes an actual default but instead restructures its debt. As mentioned in section 2.1 there are several different credit events that will trigger a default and the different events will have an influence on the recovery rate (Duffie and Singleton, 2003). The probability of default is linked to the sustainability of external debt and to problems associated with short-term illiquidity or long-run solvency. According to Duffie and Singleton (2003) factors that are likely to influence a sovereign s ability to service its debt (and the expected sign of the effect) are Current account to GDP (+) Terms of trade (+) Reserves to import (+) External debt (-) Income variability (-) Export variability (-) Inflation (-) 16

2.2. Pricing These factors will be taken into consideration when finding possible determinants for CDS and bond spreads in section 6. 2.2.2.3 Reduced Form Models The reduced form models, also named default intensity approach, have different underlying assumptions regarding default compared to the structural approach. The time of default is modeled as an exogenous event meaning the time of default is a stochastic variable and not tied to fundamentals of the balance sheet. To model the time of default, the reduced form models assigns probabilities to different outcomes of time of default. That is, reduced form modelers estimate the probability that a given sovereign does not default within a certain period, e.g. one year (Bomfim, 2005). The modeling object in the reduced form models is the intensity process λ which can have three different assumptions: 1) constant intensity, 2) deterministic intensity function, 3) stochastic intensity process. The first two assumptions are simple however restrictive in the way that unanticipated events regarding the economy or the sovereign have no effect on the default intensity of the sovereign. Letting the intensity process follow a stochastic process yields results which are more realistic and take unexpected developments into account. Regarding specific relations between the credit spread and the underlying assumptions 6 it is not within the scope of the thesis to mathematically provide these relations. Comparing the structural models with the reduced form models three factors become apparent. Firstly, the two approaches each have their pros and cons meaning analysts should be aware of the purpose of their analysis. The second factor is the applied methodology. Fixed income modelers may prefer the reduced form models because this approach has the most similarities with for instance short term interest models. On the other hand equity analyst may find the structural approach more appealing since the approach is centered around equity-based options and the fundamentals of the entity. The third factor is the empirical fit. Although the structural models have more economic intuition, these models tend not to fit the data as well as the reduced form models (Bomfim, 2005; Duffie and Singleton, 2003). 6 Assumptions regarding recovery value, the nature of interest rates and, how premiums are paid and the default intensity. 17

2.2. Pricing 2.2.3 Empirical use of models Structural models provide an intuitive framework for identifying the determinants of financial distress and loss given default. However, the fundamental problem of these models is the unobservability of the input parameters in the equation. In the model presented by Black, Scholes and Merton the spot firm value and its volatility are unobservable and proxies are typically used for these variables. Furthermore structural models often fail to produce a realistic spread for higher rated and short-term debt. At the same time lower rated firms tend to have more complicated capital structures that cause problems in implementing this type of model. According to Benkert (2004) calibrating CDS premia based on reduced form models is directly prevented by the lack of data for making specifications of the hazard rate process/intensity process. Benkert (2004) argues that the history of CDS is not long enough to provide time series of the length required to fit stochastic process reliability. At the same time he mentions that despite the rapid growth of the market there is for a considerable number of the debt issuers periods of missing observations - even for the most frequently traded entities. Since the research of Benkert (2004) was made the CDS market has developed significantly and research based on reduced form models have been made, e.g. Pan and Singleton (2008). There is however still problems with finding quality data without holes and strange fluctuations. According to Collin-Dufresne, Goldstein and Martin (2001) and Ericsson et al. (2009) reduced-form models are better suited for fitting the observed credit spreads than they are at finding the determinants of credit spreads. The model specific problems in pricing CDS premia directly can be solved by regression analysis as done by several researchers. Among these are Collin-Dufresne et al. (2001) who examined corporate bond spreads, Benkert (2004) who examined corporate CDS, Fontana and Scheicher (2010) who examined sovereign CDS and bond spreads, Longstaff, Pan, Pedersen and Singleton (2007), Pan and Singleton (2008) and Dieckmann and Plank (2011) who examined sovereign CDS spreads and Ejsing and Lemke (2010) who examined CDS spreads on sovereigns and banks. These articles will serve as a basis for the analysis of the determinants of spreads. Regression analysis has the advantage that the economic structure is kept at a level where the available amount of data is sufficient (Benkert, 2004). Even though the models have performed poorly empirically they can still be used to understand how spreads can be constructed using a quantitative model and they are very useful for detecting the different determinants of the spreads that can be used as explanatory variables in regressions. 18