The GARCH Linear SDE: Explicit Formulas and the Pricing of a Quanto CDS

18 Pages Posted: 25 Jun 2018

Date Written: June 8, 2018

Abstract

We derive an efficient closed-form approximation for the moment generating function of the integral of a mean-reverting stochastic process, following a linear SDE, which we call GARCH. We then consider a financial application, namely the pricing of a quanto CDS under stochastic intensity of default and an FX devaluation model. Numerical results are finally showcased.

Keywords: linear SDE, chaos expansion, PDE, perturbation approach, quanto CDS

JEL Classification: C63, G13

Suggested Citation

Li, Minqiang and Mercurio, Fabio and Resnick, Serge, The GARCH Linear SDE: Explicit Formulas and the Pricing of a Quanto CDS (June 8, 2018). Available at SSRN: https://ssrn.com/abstract=3188272 or http://dx.doi.org/10.2139/ssrn.3188272

Minqiang Li

Bloomberg LP ( email )

731 Lexington Avenue
New York, NY 10022
United States

Fabio Mercurio (Contact Author)

Bloomberg L.P. ( email )

731 Lexington Avenue
New York, NY 10022
United States

Serge Resnick

Independent ( email )

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