Asian Option Pricing Under a Two-Factor Stochastic Volatility with a Stochastic Long-Term Mean

Abstract

This paper studies the valuation of continuously monitored geometric Asian options under a two-factor stochastic volatility model with stochastic long-term variance levels. We derive the joint characteristic function required for continuous geometric averaging and obtain analytical pricing formulas for fixed-strike call and put options through Fourier inversion. The analytical formulas are verified by comparison with Monte Carlo simulation. Numerical experiments show that option values are particularly sensitive to the initial variance levels, while changes in the trends of the stochastic long-term means and leverage correlations also affect prices across strikes. The proposed approach extends double Heston Asian option pricing while maintaining computational tractability, and it provides a flexible method for examining the impact of time-varying long-term volatility expectations.