Pricing and Modeling Credit Derivatives Muzaffer Akat∗ Caio Ibsen Rodrigues de Almeida†

The market involving credit derivatives has become increasingly popular and ex-tremely 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 se-curities subject 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. Assuming absence of arbitrage, 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 like basket defaults