The Garch linear SDE: explicit formulas and the pricing of a quanto CDS

A new closed-form approximation is applied to quanto CDS pricing

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Minqiang Li, Fabio Mercurio and Serge Resnick derive an efficient closed-form approximation for the moment-generating function of the integral of a mean-reverting stochastic process, which follows a linear stochastic differential equation that we call generalised autoregressive conditional heteroscedasticity. We then consider a financial application, namely the pricing of a quanto credit default swap under stochastic intensity of default and a foreign exchange

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