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  

Natalie Packham

Berlin School of Economics and Law

Lutz Schloegl

affiliation not provided to SSRN

Wolfgang M. Schmidt

Frankfurt School of Finance & Management

Date Written: November 19, 2009

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 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

Suggested Citation

Packham, Natalie and Schloegl, Lutz and Schmidt, Wolfgang M., Credit Gap Risk in a First Passage Time Model with Jumps (November 19, 2009). Centre for Practical Quantitative Finance Working Paper No. 22. Available at SSRN: https://ssrn.com/abstract=1509491 or http://dx.doi.org/10.2139/ssrn.1509491

Natalie Packham (Contact Author)

Berlin School of Economics and Law ( email )

Badensche Strasse 50-51
Berlin, D-10825
Germany

HOME PAGE: http://www.packham.net

Lutz Schloegl

affiliation not provided to SSRN ( email )

Wolfgang M. Schmidt

Frankfurt School of Finance & Management ( email )

Sonnemannstra├če 9-11
Frankfurt am Main, 60314
Germany

Register to save articles to
your library

Register

Paper statistics

Downloads
162
rank
170,659
Abstract Views
1,131
PlumX