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Packham, Natalie
Schlögl, Lutz
Schmidt, Wolfgang M.
Year of Publication: 
Series/Report no.: 
CPQF Working Paper Series 21
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.
gap risk
credit spreads
credit dynamics
first passage time models
Lévy processes
general Ornstein-Uhlenbeck processes
Document Type: 
Working Paper

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