Pricing geometric Asian options with liquidity risk under a regime-switching mixed fractional Brownian motion with jumps model

This paper addresses the challenge of accurately pricing geometric Asian options within incomplete markets characterized by regime-switching dynamics, liquidity risk, and complex asset price behaviors that incorporate both jumps and long-range dependence. Existing financial models often fail to simultaneously capture these critical features, leading to potential mispricing, particularly for Asian options whose path-dependent payoffs are sensitive to sustained market conditions and liquidity constraints. We propose a novel pricing framework by developing a hybrid asset price model that integrates mixed fractional Brownian motion (MFBM) with jump diffusion. By strictly restricting the Hurst index to H∈(3/4,1), the MFBM maintains the semi-martingale property. This ensures that the model captures both long-range dependence and discontinuous shocks while remaining compatible with the risk-neutral pricing framework. Market regimes are modeled via a continuous-time Markov chain, allowing for transitions in liquidity parameters and jump intensity across economic states. To address market incompleteness arising from liquidity risk and jumps, we identify a specific equivalent risk-neutral pricing measure via the Esscher transform technique. By leveraging an extended affine structure that accommodates regime-dependent parameters, we derive the joint characteristic function of the logarithmic asset price and its geometric average. Subsequently, semi-analytical pricing formulas for both fixed- and floating-strike geometric Asian options are obtained using the Fourier cosine series expansion (COS) method. Numerical experiments confirm the accuracy and computational efficiency of our approach.