Credit gap risk in a first passage time model with jumps

• Published in: Quantitative finance Vol. 13; no. 12; pp. 1871 - 1889
• Main Authors: Packham, Natalie, Schloegl, Lutz, Schmidt, Wolfgang M.
• Format: Journal Article
• Language: English
• Published: Bristol Routledge 01.12.2013; Taylor & Francis Ltd
• Subjects: Brownian motion; Credit dynamics; Credit spreads; Derivatives; First passage time models; Gap risk; General Ornstein-Uhlenbeck processes; Leverage; Spread; Stochastic models; Stochastic volatility; Studies; Volatility
• ISSN: 1469-7688; 1469-7696
• DOI: 10.1080/14697688.2012.739729

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 swap spreads. 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 stochastic 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.