Credit Dynamics in a First Passage Time Model with Jumps

Abstract

The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we address these issues by specifying a credit quality process to be driven by an Ito integral with respect to a Brownian motion with stochastic volatility. We derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Levy-driven Ornstein-Uhlenbeck process, for which we show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the model and provide examples.

Keywords: gap risk, credit spreads, credit dynamics, first passage time models, Levy processes, general Ornstein-Uhlenbeck process

JEL Classification: G12, G13, G24, C69