Abstract: Under the stochastic volatility model, European option prices usually have no analytical solutions. Based on the theory of Malliavin calculus, this paper proposes a new asymptotic expansion method to approximate the price of such European options by expanding the stochastic volatility path around a constant volatility model. This method provides a closed-form expansion formula that can correct the mispricing problem and generalize the famous Black-Scholes-Merton (1973) formula. Inspired by Li¹, our asymptotic expansion can achieve correction terms of arbitrary order, resulting in accurate and effcient outcomes. As an illustrative example, this paper uses a stochastic volatility model based on the GARCH diffusion process in the numerical results section.