Credit Gap Risk in a First Passage Time Model with Jumps
Centre for Practical Quantitative Finance Working Paper No. 22
39 Pages Posted: 19 Nov 2009
Date Written: November 19, 2009
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 Ito 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 Levy-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.
Keywords: gap risk, credit spreads, credit dynamics, first passage time models, stochastic volatility, general Ornstein-Uhlenbeck processes
JEL Classification: G12, G13, G24, C69
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