CHEN Dachuan, LI Chenxu, . Closed-Form Expansion of Option Prices under Stochastic Volatility Model[J]. Chinese Journal of Applied Probability and Statistics, 2025, 41(2): 223-247.
Citation: CHEN Dachuan, LI Chenxu, . Closed-Form Expansion of Option Prices under Stochastic Volatility Model[J]. Chinese Journal of Applied Probability and Statistics, 2025, 41(2): 223-247.

Closed-Form Expansion of Option Prices under Stochastic Volatility Model

  • 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 \mathrmLi^1, 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.
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