Power Series Representations For European Option Prices Under Stochastic Volatility Models
In the context of stochastic volatility models, the authors study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset price process and the volatility process. They first obtain expressions for the power series' coefficients from the generalized Hull and White formula obtained in Al'os. Afterwards, they provide representations turning out from the approach for the sensitivity problem tackled by Malliavin calculus techniques. Finally, they show for several stochastic volatility models the numerical performance of the associated Monte Carlo estimators.