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

Kefan Liu, Jiangyan Peng and Chenghao Xu

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 264-284

Abstract: 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.

Keywords: Regime-switching model; Liquidity risk; Asian options; Mixed fractional Brownian motion; Fourier cosine series expansion method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:264-284

DOI: 10.1016/j.matcom.2026.05.020

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