Pricing Discretely Monitored Asian Options Under Regime-Switching and Stochastic Volatility Models with Jumps - Zhang, Weinan; Zeng, Pingping; Zhang, Gongqiu; Kwok, Yue Kuen (Journal of scientific computing, 2024)
This paper proposes a unified approach for pricing discretely monitored floating and fixed strike Asian options under a broad class of regime-switching and stochastic volatility models with jumps. The randomness in volatility can be either characterized by regime switching among discrete market states, a diffusive stochastic variance process correlated with the underlying asset price, or a random time change applied to a background process. Our approach can be applied to price financial derivatives with exotic averaging type payoffs, which goes beyond most of the existing frameworks in terms of versatility. Our success relies on the adoption of the change-of-measure approach and a dimension reduction technique. Specifically, we construct new backward recursions for Asian options that include floating and fixed strike payoffs under a wide range of regime-switching and stochastic volatility models with jumps. The Fourier-cosine series expansion and Gauss quadrature rule are applied to solve the backward recursions. The exponential convergence rate of our approach is proven theoretically and verified numerically via comprehensive error analysis. Extensive numerical experiments demonstrate that our approach is reliable, accurate, and efficient.