Credit gap risk in a first passage time model with jumps

The payoff of many credit derivatives depends on the level of credit spreads. Inparticular, credit derivatives with a leverage component are subject to gap risk, a riskassociated with the occurrence of jumps in the underlying credit default swaps. Inthe framework of first passage time models, we consider a model that addresses theseissues. The principal idea is to model a credit quality process as an Itˆo integral withrespect to a Brownian motion with a stochastic volatility. Using a representation ofthe credit quality process as a time-changed Brownian motion, one can derive formulasfor conditional default probabilities and credit spreads. An example for a volatilityprocess is the square root of a L´evy-driven Ornstein-Uhlenbeck process. The model canbe implemented efficiently using a technique called Panjer recursion. Calibration to awide range of dynamics is supported. We illustrate the effectiveness of the model byvaluing a leveraged credit-linked note.