The negative basis - Credit Default Swap contracts and credit risk during the financial crisis

Table of contents

1. Introduction

2. Trading credit risk
2.1 Basics of credit risk
2.2 Credit derivatives: Different instruments on the market
2.2.1 Asset Swaps and Total Return Swaps
2.2.2 CDO instruments
2.2.3 Credit Spread Options
2.3 Credit derivatives: CDS Contracts
2.3.1 How they work
2.3.1.1 Fundamentals
2.3.1.2 Comparison to insurance contracts
2.3.2 Pricing CDS contracts
2.3.3 Involved risks and concerns prejudices and the truth
2.3.3.1 The current use of CDS contracts
2.3.3.2 Connection of the global financial system
2.3.3.3 Risk understanding of the different market actors
2.3.3.4 CDS contracts as a speculation instrument
2.3.3.5 Different maturities of CDS payments and fat tails
2.3.3.6 The price of credit risk on the market indicated by CDS contracts
2.3.3.7 Influences on the balance sheet
2.3.3.8 The moral hazard of risk shifting
2.3.3.9 CDS contracts as a tool for other derivatives
2.3.4 CDS contracts and regulation
2.3.5 Summary

3. The negative CDS basis
3.1 The theory of the basis
3.1.1 Swap spread and Treasury spread
3.1.2 The Asset Swap spread
3.1.3 The Z Spread
3.1.4 Cash CDS Basis dynamics: Positive and negative basis trading strategies
3.1.5 Positive or negative basis causes and situations
3.1.5.1 Physical settlement CDS as the cheapest to deliver option
3.1.5.2 CDS premia are always positive
3.1.5.3 Definition of the technical default and profit realization
3.1.5.4 Bonds traded strongly below and above par and concerns of shorting cash bonds
3.1.5.5 Funding issues and counterparty risk
3.1.5.6 Coupon and premium paying differences and coupon specificities
3.1.5.7 Growth on structured finance markets and different liquidity on market segments
3.1.6 The basis smile and basis trends
3.2 Empirical study hypotheses why and where the negative basis is present
3.2.1 Larger basis in the financial crisis than before
3.2.2 Wider negative basis for bonds of lower rated companies
3.2.3 The basis develops differently between different industries
3.2.4 Analysis details, assumptions and sample choice
3.2.4.1 Sample choice and timeframe
3.2.4.2 Assumptions and simplifications
3.2.4.3 Calculations for investigating the basis
3.2.4.4 Separation of the time horizon
3.2.5 The results for the negative basis
3.2.5.1 The overall results
3.2.5.2 Rating differences
3.2.5.3 Industry differences
3.2.6 Sample results for different companies
3.2.7 The results compared with the hypotheses and possible explanations

4. Trading strategies using the negative basis during the financial crisis
4.1 A certificate for clients of a bank
4.1.1 Determinants of the certificate
4.1.2 Idea of the certificate
4.1.3 Construction of the certificate
4.1.4 Opportunities for investor and bank due to the certificate
4.1.5 Involved risks for investor and bank
4.2 Trading strategies in the banks
4.2.1 The buy and hold strategy
4.2.2 Risks and influences of the strategy

5. Conclusion

Literature

Table of figures

Figure 1: CDS pricing

Figure 2: No Arbitrage formula

Figure 3: CDS spread formula

Figure 4: CDS fixed leg

Figure 5: CDS contingent leg

Figure 6: CDS pricing

Figure 7: CDS market development from 2004 until

Figure 8: Bond yield equation

Figure 9: ASW spread formula

Figure 10: Z Spread equation

Figure 11: Basis equation

Figure 12: Fair value calculation for a bond

Figure 13: Dirty bond price calculation

Figure 14: Calculation ASW spread

Figure 15: Duration calculation for a bond with yearly coupon payment

Figure 16: Calculation of the basis

Figure 17: Average ASW spread development 03/2005 03/2010 in bp

Figure 18: Sample average 1 year and 5 year CDS spread development 03/2005 03/2010 in bp

Figure 19: Average basis development 03/2005 03/2010 in bp

Figure 20: Standard deviation of the basis development 03/2005 03/2010 in bp

Figure 21: Max/Min of the basis development 03/2005 03/2010 in bp

Figure 22: Histogram basis data for the 24 companies and two different time periods

Figure 23: Graphically average overview of the basis variables for three time periods of the basis development 03/2005 03/2010 in bp

Figure 24: Graphically average overview A rated companies of the basis variables for three time periods

Figure 25: Graphically average overview B rated companies of the basis variables for three time periods

Figure 26: Average A rated and B rated companies ASW spread development 03/2005 03/2010 in bp

Figure 27: Average A rated and B rated companies 1 year and 5 year CDS spread develop ment 03/2005 03/2010 in bp

Figure 28: Average A rated and B rated companies basis development 03/2005 03/2010 in bp

Figure 29: Average basis development for four different industries 03/2005 03/2010 in bp

Figure 30: Basis and ASW spread development Siemens 03/2005 03/2010 in bp

Figure 31: Basis and ASW spread development Coca Cola 03/2005 03/2009 in bp

Figure 32: Basis and ASW spread development Adecco 04/2006 03/2010 in bp

Figure 33: Basis and ASW spread development Kraft foods 03/2005 03/2010 in bp

Figure 34: Basis and ASW spread development Rexam 03/2006 03/2010 in bp

List of tables

Table 1: List of examined companies with rating and industry

Table 2: Time horizon separation

Table 3: Average overview of the basis variables for three time periods in bp

Table 4: Average overview A rated companies of the basis variables for three time periods in bp

Table 5: Average overview B rated companies of the basis variables for three time periods in bp

Table 6: Average Investment grade and junk status companies basis for three different time periods in bp

Table 7: Average basis for four different industries for three different time periods in bp

1. Introduction

The current developments in the credit or bond markets influenced by the financial crisis and the economic downturn revive a discussion about credit derivatives as an instrument of speculation and one cause or determinant of the financial crisis. The government bonds of Greece and other countries and the fitting Credit Default Swaps (CDS) contracts which guarantee for the nominal of the bonds have got much pres sure and volatility after the news that the countries might get problems to refinance. Currently, CDS are used to speculate against the solvency of the different govern ments. Critics look at CDS contracts as Over the counter (OTC) instruments that are not regulated and as bilateral contracts which can have a big influence on the finan cial position of market participants and on the real credit markets.

CDS contracts are mainly an instrument for investors to insure against a default of the debtor. For the seller of the CDS they are a possibility to participate in risks he perhaps could not have taken on the bond markets otherwise. These contracts separate the default risk of the debtor from the market conditions, e.g. the market interest rates. CDS contracts make it possible to only trade the credit risk of a company or a country. Therefore, CDS contracts can be an instrument to proof the bond values and an indicator for the real credit risk of the underlying.

The discussion about CDS contracts is mostly a discussion including many prejudic es and it deals with aspects from different topics which cannot be mixed. Therefore, a clear picture of advantages and disadvantages and especially values and risks of CDS is difficult to be found in the current public discussion and economic newspaper articles.

Ambitions of the thesis

This thesis is supposed to consider the questions about CDS contracts which are interesting for the public discussion. What is the role of CDS contracts before and in the financial crisis and what kind of risks are included in the CDS trading? Are they instruments which have triggered the crisis or intensified its effects? What are the differences compared to an insurance contract? Why are CDS contracts so often used by the financial institutions?

In the financial crisis bond markets and CDS markets have lost their connection. So the credit risk on both markets is valued differently: the prices of the two markets dif fered so much that some market participants used these arbitrage possibilities to earn credit risk free money for themselves and their customers. The price difference which can be earned is called “negative basis”. It can be traded with a simple combination of the underlying bond and the fitting CDS contract.

Empirically this thesis will analyze the negative basis. Where is this negative basis to be found? Do the underlying companies differ in their rating or their industry? Was the negative basis bigger during the financial crisis than before? The thesis tries to find out an explication for the basis and shows the special market circumstances.

Approach

In a first step, the trading of credit risk will be regarded theoretically. An overview of the credit risk and different instruments trading this risk will be presented. Particularly CDS contracts will be analyzed: it will be examined how they work and which risks they involve. Their role before and during the financial crisis will be assessed. This analysis will show a differentiated view on these instruments.

In a second step the negative basis will be analyzed empirically. Initially the theory of the negative basis will be explained: how it is calculated and which are the assumptions and problems for the basis. Then hypotheses will be posed, why and where the negative basis is present. Individual and overall results will be shown for some different rated companies from different industries for a longer time horizon. They will be compared to the hypotheses.

In the last step, different trading strategies for market participants will be introduced. It will be described how the negative basis can be traded and used to generate excess returns. In this section, the proprietary trading constructions of the banks will be examined. It will be developed how certificates for customers of banks are constructed. The involved risks will be presented and discussed.

As a conclusion a short summary of the results and the discussion about CDS contracts will be given.

The historical data (bond prices, CDS spreads and swap rates) for the basis investigation are all downloaded from Thomson Reuters Datastream.

2. Trading credit risk

2.1 Basics of credit risk

The credit risk or default risk means that an obligor is not able to fulfill his payments to the lender. The credit event can appear with bankruptcy of the debtor, the failure to pay, restructuring of the debtor, a downgrade of the debtor, obligation acceleration or a change in the credit spread. Credit events a rare, which mean that they occur un expectedly, bring on significant losses, and the size of the loss is unknown before the event.

The credit risk itself consists of different kinds of risks: the arrival risk, including the probability of default, the timing risk, which means the time when the real default proceeds, the recovery risk, which means how much the lender could get back in case of default and the market risk describing how the market price of the underlying¹ changes with the occurrence of a default event. Last but not least the default correla tion risk has to be considered looking at the possibility of default events of several debtors at the same time. Because of the several risk factors and the definition of the credit event the credit risk is not simple to calculate or to mitigate. To evaluate the credit risk, appropriate credit risk models are used. Also the credit ratings of the rat ing agencies which are made with in house models could be used. With credit deriva tives traded on the markets or in the OTC sector, market participants show their es timation of the current and prospective credit risk of the underlying in normal market circumstances.²

2.2 Credit derivatives: Different instruments on the market

There are several instruments to trade credit risks on the regulated markets or bilate rally between different participants (OTC). Credit derivatives have in common that they are mainly used to transfer, manage or hedge credit risk. Speculation about sol vency is also a possible cause to buy or to sell credit derivatives. For an industry company it is more interesting to hedge the risk of its own bonds or loans. Therefore, they use instruments which are connected to the credit spread and its change. Banks often use credit derivatives to participate in credit risk they could not get from their customers in their business region or industry. On the one hand banks can improve the diversification of their credit portfolio; on the other hand they can sell risks and improve their equity position (also see section 2.2.2).

Investors like hedge funds can take risks they could not take directly on the bond markets, where they would have to invest also a huge amount of money to trade these risks. Furthermore the bond market does not have the same liquidity in all in vestments and products to trade them with low spreads. The main participants in the credit derivatives market are banks, insurance companies and hedge funds. The payoff of the credit derivative instrument is affected by the credit risk of an un derlying. Roughly, the credit derivatives can be separated into two groups: the in struments which concern or transfer the credit default risk and the instruments which transfer the credit spread risk or the change of the credit worthiness of the underlying. But in many derivates the credit risk components cannot be separated this way. An underlying could be an individual loan, a structured collection of several loans or a market traded security like a bond. In the credit risk markets the underlying is called reference entity. Usually the buyer of the credit derivative buys protection against the credit event or credit spread changes. The seller of the credit derivative sells protec tion and is long in the credit risk. The seller receives a premium or a payment. The buyer has to pay for the protection or the transfer of the risk. In this section the most important credit derivatives or capital market oriented products for credit risk transfer will be examined.³

2.2.1 Asset Swaps and Total Return Swaps

Asset Swaps belong to the group of credit derivatives which trade or obtain the credit risk of the underlying e.g. a bond. Swaps are bilateral agreements to change pay ment flows between two market participants. The notional amount is not changed at any time while the contract between the partners is valid. Usually the transaction is proceeding between a bank and an institutional investor. The investor can hedge the credit risk, the interest rate risk and the currency risk with an Asset Swap. A simple Asset Swap changes the coupon payments of a bond. The investor often does not want to trade or to take the interest rate risk, because the market interest rate risk could change and as a result the market value of the underlying bond. The buyer of the Asset Swap receives e.g. the Libor +/ credit spread and pays the fixed rate of the underlying bond. The value of the Asset Swap or the actual credit risk is the spread over the Libor rate. Now the investor receives a floating rate and because of the changeable Libor rate, the interest rate risk is transferred to the bank. Asset Swaps can be considered as combined money market and credit derivative instruments. Therefore, the investor actually holds a synthetic floater. If the underlying bond is de faulted or bankrupt, the buyer continues to receive the floating interest rate. So he is secured against the default of the underlying, because the investor has changed his credit risk exposure.⁴

The Asset Swap spread has an important function on the credit market, because it can show the credit risk of the underlying itself by the spread over the Libor rate. Therefore it is an important key figure. An Asset Swap package means the simulta neous purchase of a bond and the agreement on an exchange of the cash flows. A Total Return Swap adds the market value changes of the underlying bond to the swap agreement of the contract partners. So in each period market value changes of the underlying will be calculated and differences to the period before will be ex changed between the contract partners. Therefore, a Total Return Swap is not con nected to a special credit event. All market value changes e.g. interest rate changes or rating changes of the underlying are concerned. That means Total Return Swaps can also transfer the credit spread risk beside both the interest rate risk and the de fault risk.⁵

A key feature of a swap is that the parties do not transfer the ownership of the assets. There is no transaction of the underlying between the contract partners. So the con tract partners win flexibility and need less capital to fulfill the trade. An Asset Swap allows the investors to manage active duration of portfolios and the balance sheet and to trade credit spreads. The counterparty risk should be considered, which means that the contract partner cannot fulfill his obligations, as in all bilateral OTC contracts.⁶

2.2.2 CDO instruments

Collateralized Debt Obligations (CDOs) are a category of Asset Backed Securities. ABS are securities which consist of a pool of assets like credits, loans or bonds and which are secured by these assets. In the case of CDOs the pool of assets are di vided in tranches which have different repayment priorities. By securitization loans and credits which are usually not available on the markets are made tradable. CDO products have to be separated in true sale transactions where the assets (e.g. loans, bonds) are sold and transferred, and unfunded credit derivatives where a synthetic CDO owns the credit exposure of a portfolio of assets. The assets themselves stay in the ownership of the bank or former holder. These synthetic transactions can be supported by Credit Default Swaps (see section 2.3.3.9). They can be funded or un funded. A funded synthetic CDO means that the investors pay an amount of money when the contract is fixed to secure for the default event.⁷

A synthetic CDO can be regarded as an insurance contract on a pool or index of loans or bonds with a deductible and policy limit. The deductible and limit is con structed with the different tranches. With the investment in different tranches, the lev el of protection can be chosen: which part of the losses should be borne by the inves tor and which by the product. The attachment point and the detachment point deter mine the border of protection and credit risk taking. Synthetic CDOs are very simple means to leverage the positions in the different tranches, because the capital struc ture is not predefined. In contrast to a true sale transaction the synthetic CDO con tract can theoretically be replicated in an endless way. It is possible to transact the underlying assets only one time, a synthetic transaction can in contrast be made as often as the seller wants.⁸

True sale transaction or cash CDOs are no classical credit derivatives because the securitization process actually uses the real credits or loans. Therefore, the credits and loans will be sold to a Special Purpose Vehicle (SPV) and change the owner. In this SPV several investors can invest their money in different tranches of bonds, cre dits or loans, which differ in their credit quality (e.g. rating) from the equity tranche (highest yield) up to the senior tranche (lowest yield). Like in a waterfall, the equity tranche would be touched first if the underlying defaults. After this, the different tranches up to the senior tranche would be touched.⁹

In the true sale transaction a bank or financial institution can clear the balance sheet. Credit risk exposure which does not fit can be sold so that capital can be set free to use it for other loans, to improve the diversification of the loan portfolio or to lower the necessary equity quote of the balance sheet. The bank or financial institution retains the equity tranche in most of the transactions to demonstrate the quality of the loans because the equity tranche is the first one to be touched if loans or bonds of the SPV default. If the bank was not convinced of the quality of the loans, it would not retain the tranche. This retaining reduces the asymmetric information problem between sel ler and buyer in the transaction. The bank knows much more about the credit portfo lio than an investor from outside of the bank or financial institution.¹⁰

With CDO vehicles the investor can participate in risks he probably cannot take in his usual business or on the financial market. Imagine a bank which has a very regional and special loan portfolio: buying a tranche of a CDO can help to diversify the loan portfolio. Therefore, unsystematic risk can be reduced. As a result the equity of the bank can be reduced or the lending can be increased.

A problem in these contracts is the valuation of the several loans and tranches. Es pecially the correlations between the different probabilities of default are complicated to simulate and identify. With the number of assets the complexity of the valuation is also growing. In the financial crisis the pools of assets led to a massive depreciation potential in the bank’s balance sheets. Rating Agencies assessed high ratings (above A) for these instruments in the whole pool of loans, although there were loans with lower ratings in the pool. During the financial crisis it was not possible to eva luate the CDO accurately because there were almost no transactions in this time frame and the defaulted loans could not been evaluated or sold. So the liquid market of issuing and selling CDOs became very fast very illiquid for a first time. The default of many different loans in the pool also led to the default of technically safer and downstream tranches. That actually means big losses for the owners of these tranches. The correlations of simultaneous defaulting were underestimated and the credit risk was not regarded adequately.¹¹

Overall a synthetic CDO can be seen as a further possibility for the seller to transfer the credit risk to a tradable product. Particularly the securitization and pooling of loans or bonds made this kind of products interesting for institutional investors and banks all over the world. The CDOs can be seen as one of the main financial instru ments of the financial crisis, because they consisted of the real estate loans which defaulted or lost a lot of value and so can be regarded as the trigger of the crisis. Nevertheless CDOs are just instruments of trade, but they have to be evaluated by investors and rating agencies in the right way. From the view of the financial markets CDOs complete the market and make untradeable assets tradable.

2.2.3 Credit Spread Options

With Credit Spread Options the credit spread risk is tradable. Credit Spread Options are compensated in case of a predefined credit event with a predefined payment. For this compensation a premium has to be paid during the lifetime of the option. It is typ ical for an option that it is possible for the buyer of the option to participate in changes of the underlying price during the lifetime of the option which is influenced by the creditworthiness. That means for example if the credit quality of the underlying is falling and consequently the credit spread becomes bigger, the value of the option will increase. If the spread at maturity is bigger than the strike spread, the buyer will trigger the option. Therefore, the Credit Spread Options belong to the group of credit derivatives which only secure for credit spread changes, but not for the actual no minal of the underlying. Nevertheless, if the underlying is nearly defaulted, the credit spread will also increase dramatically.¹²

The Credit Spread Option is not connected to the underlying capital. That means the credit risk can be traded separately from the nominal. The capital amount which is necessary is smaller than the transaction of buying the underlying and participating in the credit risk. Speculation on credit risk or hedging the credit spread risk is possible in this category of credit derivatives as well.

2.3 Credit derivatives: CDS Contracts

2.3.1 How they work

2.3.1.1 Fundamentals

Compared to the described credit derivatives, Credit Default Swap (CDS) contracts only secure for the default of the underlying. During the lifetime of the CDS contract the buyer of the CDS pays a premium. The seller of the CDS receives the premium and secures at each point of time for the nominal of the loan or bond. The premium or CDS spread is quoted in basis points per annum of the notional amount of the un derlying. Therefore, a CDS contract can be regarded as an insurance contract which is tradable. The premium for the original holder of the contract does not change over time and is calculated in advance. CDS contracts are bilateral and are mostly nego tiated and traded OTC. For an investor or buyer, CDS contracts mean to guarantee the transfer of the whole default risk. In contrast to interest rate swaps, the risk for the two participants in the contract is not symmetric. Like options, the CDS contracts can imply a liability risk up to the whole nominal of the underlying for the seller. The buyer only takes the risk of losing all premiums paid in the lifetime of the contract if the un derlying does not default.¹³

Even if he believes in a default of the underlying, he can stay invested in the bond or loan and receives a constant stream of interest payments. The CDS does not protect against changes in the credit spread and in the market value of the loan or bond during the lifetime of the contract. A default of the underlying is mostly no surprise; it is a continuing development. The financial distress and the process leading to the default can be observed. This can be looked at in the credit spreads of the underlying and tracked with the new CDS premia.

If the CDS contract is compared to products on the bond market or if a synthetic reproduction of the instrument is searched, following relationship holds:

Figure 1: CDS pricing 1

illustration not visible in this excerpt

Source: Coleman, 2009.

And vice versa algebraic signs for the CDS buy position. This relationship shows that the CDS spread or price could be seen as the credit spread of the underlying and make it possible to trade the default risk without buying and selling two securities si multaneously.¹⁴ For many investors there is no possibility to be short in a bond. Therefore, CDS contracts complete the market for these investors. More advantages of the CDS contracts compared to other credit derivatives are the clear separation of credit and interest rate risk and the simple possibility to connect the contract with other products in a synthetic combination. It is also possible to ne gotiate about contracts with a completely different maturity than the underlying bond. Therefore, a CDS contract can only secure for the default of the reference entity for example for two years, when the bond has a maturity of 4 years. Because of the separation of contract and underlying it is also possible to trade the contracts during the whole lifetime. For banks, which are typically net buyers of CDS, the contracts can lead to reduced equity requirements. Before the purchase of a CDS contract, the bank has to deposit the equity amount for the underlying credit or loan fitting to the rating. After buying a CDS contract, the bank can weight the deposit eq uity with a factor for the counterparty (e.g. another bank). Therefore, the deposit equi ty amount is smaller and the bank can use the capital for different purposes.¹⁵

2.3.1.2 Comparison to insurance contracts

Unlike insurance companies, the contract partners of the CDS are not regulated. That means the CDS seller does not have to diversify the risk of his contracts or to hold a certain amount of equity to trade these contracts. The seller is free in his risk management and objective for the contract. So the risk of non payment of the seller in the case of default has to be carried completely by the buyer of the CDS named counterparty risk.

Owning the underlying security is not necessary to close a CDS contract. If some thing shall be insured by an insurance contract, the concerned asset or right has to be owned by the policy holder. There is an additional important difference between insurance products and CDS contracts. On the one hand the classical insurance has no big changes in the probability of the insured event; on the other hand the CDS underlying default probability can change dramatically during the lifetime of the con tract. Comparable is that in case of a loss the premium of the CDS contract will be adjusted to a higher amount of payment as well as an insurance contract premium.¹⁶ Furthermore different accounting standards are responsible for insurance and CDS contracts. The applied rules for accounting can differ vastly, so that CDS and insur ance contract show a different appearance of the balance sheet in the end.¹⁷ If the underlying defaults, there are two possibilities of compensating the buyer of the CDS contract: Either the buyer delivers the physical bond to the seller and the seller, in exchange, pays the nominal cash amount or the seller pays the difference of no tional of the underlying and a possible recovery amount. Often the buyer of the CDS contract does not hold the underlying and cannot deliver it. So a pure cash settle ment is appropriate.¹⁸

The Credit Derivative contracts can also be completely funded. In this case the de rivative contract is called Credit Linked Note (CLN). The protection buyer is the issuer of the note. In the beginning the protection seller pays an amount to the issuer, the price of the CLN. If the reference entity does not default, the amount, the nominal, is paid back at maturity of the contract to the investor, the protection seller. If the under lying has a credit event, an amount less than the nominal is paid back to the investor. The amount is reduced by the redemption amount of the linked reference entity.¹⁹

CDS contracts can be negotiated individually. That means, the credit event can be fixed in the contract and does not have to be coincident with the real default event of the underlying. For example, the credit event for the CDS could be a special event that is likely to bring about the loss of the nominal. Usually the credit event is based on information which is official and available for the public. In this way, the credit event is objective for the contract partners. In contrast to insurance contracts, a deductible fixed in the contract is not possible.

The realization before the end of the lifetime is possible for CDS contracts: but the advance termination needs the approval of the contract partners. The investor pays the current market value as a termination fee. Future premium differences are paid, discounted and multiplied with the probability of default and the notional value. It is also possible to transfer the contract to third parties. That needs an approval of the corresponding counterparty, too. The third possibility is to setup an offsetting long or short position.²⁰

Another sub category of Default Swaps is the Default Digital Swap. The DDS seller gives a predefined amount of payment in case of default to the buyer as compensation. Therefore, the expected recovery rate is redundant to find the compensatory payment and the premium or spread of the contract.²¹

2.3.2 Pricing CDS contracts

The premium which has to be paid for a CDS contract is also called CDS Spread, because it is the credit risk spread of the underlying and must be added to the inter est payment of a secured bond or loan, if the whole return of the bond or loan is con sidered.

There is not only one valuation model for CDS contracts on the market. Different market participants are using several modified models for the calculation of the premium of the CDS. Important factors for the pricing are also the current market liquidity and the relationship to the customer if the contract is transacted between a bank and an investor. Investors and traders get different quotations. The trader can decide which position he wants for himself in the market, for example if he wants to take an aggressive position there. The risk management will influence the pricing for the seller of the contract, too. For the seller it is important to oversee his own risk bearing ability each time he trades on the markets.²²

To calculate the premium of a CDS contract, several input factors are necessary. Most important and critical are the probability of default and the expected recovery amount of the underlying. In many cases it needs a long time before the recovery amount can be fixed after defaulting. That means in practice, that after the defaulting of the underlying the phase of restructuring or selling the assets starts. In this process, the recovery amount for the holder of bonds and loans is determined. Sometimes a Dutch auction is used to determine the price of the assets after default ing. The asking price is lowered until someone accepts it for the assets, or the reser vation price is reached. The potential investor uses the highest price he just wants to pay for the assets of the underlying. After this the recovery amount is settled, and the final payments of the CDS contract will be transacted.²³

The probability of default as an input factor can be defined for the individual underly ing (e.g. company bond, government bond) by individual modified models. In most of the cases, the first step is to analyze the credit risk aspects of the underlying and/or to use external ratings from rating agencies. Usually, the probability of default is re ferred to the following twelve months. For calculating the probability of default of an individual reference entity, qualitative inputs like the industry, the size, the region, the competition in the industry, the kind of loan or bond and the rank of the bond or loan can be used. Also quantitative figures and ratios of the balance sheet, the profit and loss structure or macroeconomic influences can be considered.²⁴

For many entities the default probability curve is available at market information systems like Bloomberg. The default probabilities are calculated with the CDS spread curve of the market. That means a curve is abstracted for different maturities of comparable CDS contracts. For price predictions during the lifetime of the contract a model assumption makes sense as well: for example a geometric Brownian motion with negative jumps to simulate the firm`s value over time. Early models which used the Brownian motion did not include the possibility of jumps in the asset value process. If a predetermined barrier is touched in this value process over time, the underlying is defaulted. With the volatility and jumps model of an individually underlying it is possible to explain 50% of the CDS price variations.²⁵

The CDS contract itself consists from the mathematical point of view of two different payment flows. The buyer of the contract pays the periodical payment which is called fee leg and the seller pays in the case of the predefined credit event the compensato ry contingent leg.

Figure 2: No Arbitrage formula

illustration not visible in this excerpt

Source: Beck, The CDS market: A primer, 2009.

PVfix means the present value fee leg which includes the fixed payments in the life time of the contract. PVcont is the present value of the compensation payment in the case of the credit event. These payment flows should have the same amount or in other words the present value of these payments should be the same for a fair transaction. For these payments the following equation is used:

Figure 3: CDS spread formula

illustration not visible in this excerpt

Source: Beck, The CDS market: A primer, 2009.

Expressed in a basic equation, the CDS Spread (premium) S should be the same as the compensation amount (nominal minus recovery amount) 1 R multiplied by the default probability p. If the Spread is used, the following formula can be developed:

Figure 4: CDS fixed leg

illustration not visible in this excerpt

Source: Beck, The CDS market: A primer, 2009.

The first half of the formula shows the discounted premium payments if no default occurs. N gives maturity in years, D is here the discount factor for the different time periods, q is the survival probability (no credit event occurs in the period), S is the CDS Spread and d the fractions the premium is paid in (d=1 for yearly payments, d=0.5 for half yearly payments).

The second part of the formula shows the accrued payment if the default occurs between payment dates of the premium.

Figure 5: CDS contingent leg

illustration not visible in this excerpt

Source: Beck, The CDS market: A primer, 2009.

This formula consists of the compensation payment 1 R and the probability of default in the respective period. If the two present values will be calculated, the difference should be zero and a fair value for the CDS Spread can be calculated.²⁶

There is also the possibility to fix the price of new issued CDS contracts using the CDS spreads known from the markets. Like for newly issued options the newly issued contract gets his price from comparable available contracts. An implied prob ability of default curve is used. Input factors are the market available CDS contracts and their spreads. The price is then adjusted for differences in maturities and special content of the contract.²⁷

Another possibility to evaluate a CDS contract and find a fair premium is to derive the price from the Asset Swap spreads on the market. Following coherence should hold:

Figure 6: CDS pricing 2

illustration not visible in this excerpt

Source: Coleman, 2009.

The fixed rate bond bears the interest rate risk and the credit risk of the underlying corporate. If the riskless bond is sold, only the credit risk has to be borne by the seller. The credit spread then results in the CDS spread or premium. This pricing of the con tract supposes the arbitrage free assumption on the market. But it has to be consi dered that for fixed rate bonds with significant discount or premium this relationship does not hold in any case. Even the connection between the bond market and the CDS market is not guaranteed, so that they show the same prices for the credit risk (see also section 3.1).²⁸

2.3.3 Involved risks and concerns prejudices and the truth

In the discussion about the financial crisis and the role of CDS contracts many risks and concerns are presented. But many of them are not discussed seriously or they are dealt with in a wrong context. This subchapter shall list several of them and show different views on the concerns and topics.

2.3.3.1 The current use of CDS contracts

If the main task of financial markets is regarded, CDS contracts have an important role. As one of the financial innovations they complete the financial markets. Inves tors who do not want to hold a risk can transfer it to different market participants who want to bear the risk and complete their risk exposure with these instruments.

Therefore, CDS contracts are an instrument of risk management or a possibility to enhance the interest rate income. Indeed, CDS contracts are also used to speculate about the credit worthiness of an underlying. More precisely, with CDS contracts it is possible to be short in the credit market. When the CDS contract is bought, the pre mium is fixed for the buyer. On the secondary market it is possible to trade this CDS contract and earn money if the credit worthiness is deteriorated during the holding period of the contract. In the current case of Greece, this speculation means that for example hedge funds take the position of the buyer of the CDS contracts. They wait for bad news on the markets about a worse condition of the Greece government`s loan exposure. In the case of Greece bad news mean e.g. a depreciation of the rat ings of the government bonds down to non investment grade. Many investors are not allowed by their investment rules to invest in non investment grade bonds like pension funds. They had to sell the bonds which pushed down the prices of the bonds further on.²⁹ Therefore, a downward spiral can be started: A lower bond price makes the market participants insecure and leads to a further selling of the bonds. The refinancing process for the reference entity becomes more and more difficult and expensive.

Important is to mention that speculation with CDS contracts has the same result as any other derivative trading: it is a zero sum game. That means one of the contract partners of the bilateral agreement has to pay to the other side when the lifetime of the contract ends. One side is winning, whereas the counterparty has to lose. In this way, hedge funds or banks often speculate against each other, and nobody else is part of this speculation. Consequently it is not possible to talk about speculators as a homogeneous group.³⁰

Hedge funds often prefer CDS contracts to bonds because of the higher liquidity in these contracts compared to the underlying bond market for every maturity. They estimate the simple possibility to be short in the credit risk and the comparable small amount of money which is necessary to enter the contract.

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¹ An underlying can be any kind of bond, a package of loans or an individual non market traded loan

² Cf. Schlögl, 2003.

³ Cf. Hofmann, Rudolph, Schaber, & Schäfer, 2007, p.67.

⁴ Cf. Pereira, 2003.

⁵ Cf. Schlögl, 2003.

⁶ Cf. Choundry, The credit default swap basis: illustrating positive and negative basis arbitrage trades, 2006.

⁷ Cf. Melennec, 2000.

⁸ Cf. Ding & Sherris, 2009.

⁹ Cf. Hofmann, Rudolph, Schaber, & Schäfer, 2007, p.40/41/42, cf. Benmelech & Dlugosz, 2009, p.619.

¹⁰ Cf. Benmelech & Dlugosz, 2009, cf. Morkötter & Westerfeld, 2008.

¹¹ Cf. Crotty, 2008, pp.27/30.

¹² Cf. Hofmann, Rudolph, Schaber, & Schäfer, 2007, p.70/71. 8

¹³ Cf. Mengle, 2007.

¹⁴ Cf. Coleman, 2009.

¹⁵ Cf. Depecker, 2009.

¹⁶ Cf. Coleman, 2009.

¹⁷ Cf. Garbowski, 2009.

¹⁸ Cf. Hofmann, Rudolph, Schaber, & Schäfer, 2007, p.8.

¹⁹ Cf. Choundry, The credit default swap basis: illustrating positive and negative basis arbitrage trades, 2006, p.6.; cf. Galiani, Gallo, Jonson, & Kakodkar, 2006.

²⁰ Cf. Kroll, 2009.

²¹ Cf. Schlögl, 2003.

²² Cf. Kroll, 2009.

²³ Cf. Kibbe, Fu, & Grady, 2008; cf. Mengle, 2007, p.19.

²⁴ Cf. N.N., Definition of Probability of Default; cf. official Standard & Poors PD template.

²⁵ Cf. Zhang, Zhou, & Zhu, 2005.

²⁶ Cf. Beck, 2009.

²⁷ Cf. Nencioni & Xu, 2000.

²⁸ Cf. Coleman, 2009.

²⁹ Cf. Meier, 2010.

³⁰ Cf. Dickinson, 2008, p.22.