Fast Valuation and Calibration of Credit Default Swaps Under Levy Dynamics

22 Pages Posted: 22 Jun 2010

See all articles by Fang Fang

Fang Fang

FF Quant Advisory; Delft University of Technology

Henrik Jönsson

European Institute for Statistics, Probability, Operations Research and their Applications (EURANDOM)

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: February 18, 2009

Abstract

In this paper we address the issue of finding an efficient and flexible numerical approach for calculating survival/default probabilities and pricing Credit Default Swaps under advanced jump dynamics. We have chosen to use the firm's value approach, modeling the firm's value by an exponential\levy\model. For this approach the default event is defined as a first passage of a barrier and it is therefore possible to exploit a numerical technique developed to price barrier options under\levy\models to calculate the default probabilities. The method presented is based on the Fourier-cosine series expansion of the underlying model's density function.

With this method we calibrate two well known\levy\models, the Normal Inverse Gaussian and the CGMY, to the market quotes of the iTraxx Series 7 and 8 constituents. In the calibration study we look at the root mean square error of the fit and find that both models give a very good fit to market data. Furthermore, we investigate how the out of calibration given parameters evolve over the year covered by the two series. Finally, we look at the changes in the default probability term structure over the year.

Keywords: Levy processes,Credit risk, Default probability, Credit Default Swaps, Fourier-cosine expansion

JEL Classification: C02, C15, C63, G12

Suggested Citation

Fang, Fang and Jönsson, Henrik and Oosterlee, Cornelis W. and Schoutens, Wim, Fast Valuation and Calibration of Credit Default Swaps Under Levy Dynamics (February 18, 2009). Available at SSRN: https://ssrn.com/abstract=1628672 or http://dx.doi.org/10.2139/ssrn.1628672

Fang Fang

FF Quant Advisory ( email )

De Corridor 5
Breukelen, 3621ZA
Netherlands

HOME PAGE: http://https://fsquaredquant.nl/

Delft University of Technology ( email )

Stevinweg 1
Stevinweg 1
Delft, 2628 CN
Netherlands

Henrik Jönsson (Contact Author)

European Institute for Statistics, Probability, Operations Research and their Applications (EURANDOM) ( email )

P.O Box 513
Eindhoven, 5600 MB
Netherlands

HOME PAGE: http://www.eurandom.nl

Cornelis W. Oosterlee

Utrecht University - Faculty of Science

Vredenburg 138
Utrecht, 3511 BG
Netherlands

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

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