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Packham, Natalie
Schlögl, Lutz
Schmidt, Wolfgang M.
Year of Publication: 
Series/Report no.: 
CPQF Working Paper Series 22
The payoff of many credit derivatives depends on the level of credit spreads. In particular, credit derivatives with a leverage component are subject to gap risk, a risk associated with the occurrence of jumps in the underlying credit default swaps. In the framework of first passage time models, we consider a model that addresses these issues. The principal idea is to model a credit quality process as an Itô integral with respect to a Brownian motion with a stochastic volatility. Using a representation of the credit quality process as a time-changed Brownian motion, one can 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. The model can be implemented efficiently using a technique called Panjer recursion. Calibration to a wide range of dynamics is supported. We illustrate the effectiveness of the model by valuing a leveraged credit-linked note.
gap risk
credit spreads
credit dynamics
first passage time models
stochastic volatility
general Ornstein-Uhlenbeck processes
Document Type: 
Working Paper

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