Credit Modelling Under Jump Diffusions with Exponentially Distributed Jumps - Stable Calibration, Dynamics and Gap Risk

22 Pages Posted: 15 Sep 2010 Last revised: 8 Oct 2015

See all articles by Stefan Kassberger

Stefan Kassberger

Frankfurt School of Finance & Management gemeinnützige GmbH

Martin Hellmich

Frankfurt School of Finance & Management gemeinnützige GmbH

Wolfgang M. Schmidt

Frankfurt School of Finance & Management

Date Written: September 13, 2010

Abstract

This paper introduces a structural credit default model that is based on a hyper-exponential jump diffusion process for the value of the firm. For credit default swap prices and other quantities of interest, explicit expressions for the corresponding Laplace transforms are derived. As an application of our findings, the model is calibrated to market quotes of fair credit default swap spreads. The time-dynamics of the model are studied, particularly the jumps in credit spreads, the understanding of which is crucial for the valuation of options on credit default swaps such as gap options.

Keywords: credit default, structural model, credit default swap, hyper-exponential jump diffusion, spectrally negative Kou process, entropy-based calibration

JEL Classification: G12, G13, G24, C69

Suggested Citation

Kassberger, Stefan and Hellmich, Martin and Schmidt, Wolfgang M., Credit Modelling Under Jump Diffusions with Exponentially Distributed Jumps - Stable Calibration, Dynamics and Gap Risk (September 13, 2010). Available at SSRN: https://ssrn.com/abstract=1676688 or http://dx.doi.org/10.2139/ssrn.1676688

Stefan Kassberger

Frankfurt School of Finance & Management gemeinnützige GmbH ( email )

Sonnemannstraße 9-11
Frankfurt am Main, 60314
Germany

Martin Hellmich

Frankfurt School of Finance & Management gemeinnützige GmbH ( email )

Sonnemannstraße 9-11
Frankfurt am Main, 60314
Germany

Wolfgang M. Schmidt (Contact Author)

Frankfurt School of Finance & Management ( email )

Sonnemannstraße 9-11
Frankfurt am Main, 60314
Germany

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