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

See all articles by Natalie Packham

Natalie Packham

Berlin School of Economics and Law; Humboldt University Berlin

Lutz Schloegl

affiliation not provided to SSRN

Wolfgang M. Schmidt

Frankfurt School of Finance & Management

Date Written: August 1, 2010

Abstract

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

Suggested Citation

Packham, Natalie and Schloegl, Lutz and Schmidt, Wolfgang M., Credit Dynamics in a First Passage Time Model with Jumps (August 1, 2010). CPQF Working Paper Series No. 21, Available at SSRN: https://ssrn.com/abstract=1476761 or http://dx.doi.org/10.2139/ssrn.1476761

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

Humboldt University Berlin ( email )

Unter den Linden 6
Berlin, AK Berlin 10099
Germany

Lutz Schloegl

affiliation not provided to SSRN ( email )

Wolfgang M. Schmidt

Frankfurt School of Finance & Management ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
118
Abstract Views
1,192
rank
324,399
PlumX Metrics