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|Title:||Credit dynamics in a first passage time model with jumps |
Schmidt, Wolfgang M.
|Issue Date:||2009 |
|Series/Report no.:||CPQF Working Paper Series 21|
|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.|
first passage time models
general Ornstein-Uhlenbeck processes
|Document Type:||Working Paper|
|Appears in Collections:||CPQF Working Paper Series, Frankfurt School of Finance and Management|
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