PRICING POWER OPTIONS UNDER STOCHASTIC VOLATILITY

Abstract

We study the pricing of European power options in a market where the underlying asset is driven by a fast mean-reverting stochastic volatility factor, which captures empirically observed features such as volatility clustering and mean reversion that are absent in the classical Black-Scholes framework. Using singular perturbation techniques, we derive an asymptotic pricing formula for the price of the power option. The resulting approximation yields a semi-analytic pricing formula that preserves much of the tractability of the constant-volatility power option formula while reflecting more realistic volatility dynamics. Furthermore, to evaluate the performance of the approximation, we conduct Monte Carlo simulations of the stochastic volatility model and use the simulated prices as benchmark values. The numerical results show that the correction significantly improves accuracy, with the approximate prices closely matching the Monte Carlo benchmarks. This demonstrates that the proposed asymptotic method offers an efficient and reliable tool for pricing power options under fast mean-reverting stochastic volatility.