This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density
of the underlying asset price in multidimensional stochastic volatility models. In particular, the integrationbyparts
formula in Malliavin calculus and the pushdown of Malliavin weights are effectively applied. We provide
an expansion formula for generalized Wiener functionals and closedform approximation formulas in stochastic
volatility environment. In addition, we present applications of the general formula to expansions of option prices
for the shifted lognormal model with stochastic volatility. Moreover, with some results of Malliavin calculus
in jumptype models, we derive an approximation formula for the jumpdiffusion model in stochastic volatility
environment. Some numerical examples are also shown.
