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 2628 dokane@lehman.com Stuart Turnbull +1 212 526 9251 sturnbul@lehman.com

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 and justify 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. The default 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 complete study 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.

2

THE CREDIT DEFAULT SWAP

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 to