Pricing long-maturity equity and FX dervatives with stochastic interest rates and stochastic volatility

In this paper we extend the stochastic volatility model of Schöbel and Zhu (1999) by including stochastic interest rates. We allow all driving model factors to be instantaneously correlated witheach other, i.e. we allow for a general correlation structure between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options eciently and in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization of the model and show how the pricing of forward starting options can be performed. Finally, weconclude.

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