The GARCH Linear SDE: Explicit Formulas and the Pricing of a Quanto CDS
18 Pages Posted: 25 Jun 2018
Date Written: June 8, 2018
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
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