Default Swap Games Driven by Spectrally Negative Levy Processes

Stochastic Processes & their Applications, 123(2): 347-384, 2013.

33 Pages Posted: 26 Feb 2012 Last revised: 8 Jan 2013

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Kazutoshi Yamazaki

Kansai University - Department of Mathematics

Masahiko Egami

Kyoto University

Date Written: February 22, 2012

Abstract

This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Levy processes, we apply the principles of smooth and continuous fit to identify the equilibrium exercise strategies for the buyer and the seller. We then rigorously prove the existence of the Nash equilibrium and compute the contract value at equilibrium. Numerical examples are provided to illustrate the impacts of default risk and other contractual features on the players’ exercise timing at equilibrium.

Keywords: optimal stopping games, Nash equilibrium, Levy processes, scale function, default swaps

JEL Classification: C73, G13, G33, D81

Suggested Citation

Leung, Tim and Yamazaki, Kazutoshi and Egami, Masahiko, Default Swap Games Driven by Spectrally Negative Levy Processes (February 22, 2012). Stochastic Processes & their Applications, 123(2): 347-384, 2013.. Available at SSRN: https://ssrn.com/abstract=2009664 or http://dx.doi.org/10.2139/ssrn.2009664

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Kazutoshi Yamazaki

Kansai University - Department of Mathematics ( email )

3-3-35 Yamate-cho, Suita-shi
Osaka, 564-8680
Japan

HOME PAGE: http://https://sites.google.com/site/kyamazak/

Masahiko Egami

Kyoto University ( email )

Yoshida-Honmachi
Sakyo-ku
Kyoto, 606-8501
Japan

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