An asymptotic valuation for the option under a general stochastic volatility

This article examines the valuation problem for the European option under a general stochastic volatility in a certain approximate sense by adopting the small disturbance asymptotic theory developed by Kunitomo and Takahashi [25, 26]. The option value can be decomposed into the Black and Scholes value under deterministic volatility and adjustment terms driven by the randomness of the volatility, which also extends some portions of Kunitomo and Kim [24].