Credit Dynamics in a First Passage Time Model with Jumps
CPQF Working Paper Series No. 21
21 Pages Posted: 23 Sep 2009 Last revised: 13 Aug 2010
Date Written: August 1, 2010
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 address these issues by specifying a credit quality process to be driven by an Ito integral with respect to a Brownian motion with stochastic volatility. We 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, for which we show that jumps in the volatility translate into jumps in credit spreads. We examine the dynamics of the model and provide examples.
Keywords: gap risk, credit spreads, credit dynamics, first passage time models, Levy processes, general Ornstein-Uhlenbeck process
JEL Classification: G12, G13, G24, C69
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