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| Credit Dynamics in a First Passage Time Model with Jumps by Natalie Packham of the Frankfurt School of Finance & Management, September 2009 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 extend the model introduced in [Overbeck and Schmidt, 2005] to address these issues. In the extended a model, a credit quality process is driven by an Itô integral with respect to a Brownian motion with stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, we derive formulas for conditional default probabilities and credit spreads. An example for a volatility process is the square root of a Lévy-driven Ornstein-Uhlenbeck process. We show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the OS-model and the extended model and provide examples. JEL Classification: G12, G13, G24, C69. AMS Classification: 60G35, 60H05, 91B28. Keywords: gap risk, credit spreads, credit dynamics, first passage time models, Lévy processes, general Ornstein-Uhlenbeck processes. Books Referenced in this paper: (what is this?)
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