 Credit gap risk in a first passage time model with jumpsNatalie Packham, Lutz Schlögl and Wolfgang M. Schmidt No 22, CPQF Working Paper Series from Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF) Abstract: 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. Keywords: gap risk; credit spreads; credit dynamics; first passage time models; stochastic volatility; general Ornstein-Uhlenbeck processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:zbw:cpqfwp:22 Access Statistics for this paper More papers in CPQF Working Paper Series from Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF) Contact information at EDIRC. |
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