Pricing Asian options under the mixed fractional Brownian motion with jumps

F. Shokrollahi, D. Ahmadian and L.V. Ballestra

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 226, issue C, 172-183

Abstract: The mixed fractional Brownian motion (mfBm) has gained popularity in finance because it can effectively model long-range dependence, self-similarity, and is arbitrage-free. This paper focuses on mfBm with jumps modeled by the Poisson process and derives an analytical formula for valuing geometric Asian options. Additionally, approximate closed-form solutions for pricing arithmetic Asian options and arithmetic Asian power options are obtained. Numerical examples are provided to demonstrate the accuracy of these formulas, which rely on a convenient approximation of the option strike price. The proposed approximation demonstrates significantly higher computational efficiency compared to Monte Carlo simulation.

Keywords: Mixed fractional Brownian motion; Asian options; Asian power options; Jump-diffusion (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:226:y:2024:i:c:p:172-183

DOI: 10.1016/j.matcom.2024.06.014

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