Pricing and modeling credit derivatives

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The market involving credit derivatives has become increasingly popular and extremely liquid in the most recent years. The pricing of such instruments offers a myriad of new challenges to the research community as the dimension of credit risk should be explicitly taken into account by a quantitative model. In this paper, we describe a doubly stochastic model with the purpose of pricing and hedging derivatives on securities sub ject to default risk. The default event is modeled by the first jump of a counting process Nt , doubly stochastic with respect to the Brownian filtration which drives the uncertainty of the level of the underlying state process conditional on no-default event. By assuming a condition slightly stronger than no arbitrage, i.e., that there is no free lunch with vanishing risk (NFLVR) from Delbaen and Scharchermayer (1994), we provide all the possible equivalent martingale measures under this setting. In order to illustrate the method, two simple examples are presented: the pricing of defaultable stocks, and a framework to price multi-name credit derivatives such as basket defaults.

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