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Fixed Income Quantitative Credit Research April 2003

Valuation of Credit Default Swaps
Dominic O’Kane and Stuart Turnbull

Marking default swap positions to market requires a model. We present and discuss the model most widely used in the market.

Lehman Brothers | Quantitative Credit Research

April 2003

Valuation of Credit Default Swaps
Dominic O’Kane +44 (0) 20 7260 Stuart Turnbull +1 212 526 9251

We present the market standard pricing model for marking credit default swap positions to market. Our aim is first to explain why credit default swaps require a valuation model, and then to explain the standard model – the one most widely used in the market. In the process of setting out the model, we take care to explain andjustify the various modeling assumptions made. We also provide examples. 1 INTRODUCTION 1

The credit default swap is a simple derivative contract that has revolutionized the trading of credit risk. Over the past five years it has become the most widely used credit derivative product, representing about 72.5% of a total outstanding market notional currently estimated to be around $2.3 trillion2. Thedefault swap market is truly global, with contracts linked to the credit risk of a wide array of US, European and Asian corporate names as well as to a number of sovereigns. The point of this paper is to present a complete and practical exposition of the market standard model and so help those new to credit derivatives to be able to value default swap positions. We intend to publish a more completestudy of the valuation and risk management of credit default swaps shortly and we refer the reader to that for many of the technical details omitted from this abridged paper.



Credit default swaps (CDS) have been explained in detail elsewhere3. In brief, a CDS is used to transfer the credit risk of a reference entity (corporate or sovereign) from one party toanother. In a standard CDS contract one party purchases credit protection from another party, to cover the loss of the face value of an asset following a credit event. A credit event is a legally defined event that typically includes bankruptcy, failure-to-pay and restructuring. This protection lasts until some specified maturity date. To pay for this protection, the protection buyer makes a regularstream of payments4, known as the premium leg, to the protection seller as shown in Figure 1. This size of these premium payments is calculated from a quoted default swap spread which is paid on the face value of the protection. These payments are made until a credit event occurs or until maturity, whichever occurs first.

1 2 3 4

We thank Arthur Berd, Jordan Mann, Marco Naldi, Lutz Schloegland Minh Trinh for comments and suggestions. Risk Magazine Credit Derivatives Survey, February 2003. See Credit Derivatives Explained, Lehman Brothers Fixed Income Research, March 2001. The normal frequency of payments is quarterly, although payments can be monthly or semi-annual.

Please see important analyst certifications at the end of this report. QCR Quarterly, vol. 2003-Q1/Q2 1

LehmanBrothers | Quantitative Credit Research

April 2003

Figure 1.

Mechanics of a default swap premium leg

Between trade initiation and default or maturity, protection buyer makes regular payments of default swap spread to protection seller
Default swap spread Protection Buyer Protection Seller

If a credit event does occur before the maturity date of the contract, there is a payment bythe protection seller, known as the protection leg. This payment equals the difference between par and the price of the cheapest to deliver5 (CTD) asset of the reference entity on the face value of the protection and compensates the protection buyer for the loss. It can be made in cash or physically settled format. This is shown in Figure 2.
Figure 2. The protection leg following a credit event...