Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps

Foad Shokrollahi, Davood Ahmadian and Luca Vincenzo Ballestra

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Abstract: The mixed fractional Brownian motion ($mfBm$) has become quite popular in finance, since it allows one to model long-range dependence and self-similarity while remaining, for certain values of the Hurst parameter, arbitrage-free. In the present paper, we propose approximate closed-form solutions for pricing arithmetic Asian options on an underlying described by the $mfBm$. Specifically, we consider both arithmetic Asian options and arithmetic Asian power options, and we obtain analytical formulas for pricing them based on a convenient approximation of the strike price. Both the standard $mfBm$ and the $mfBm$ with Poisson log-normally distributed jumps are taken into account.

Date: 2021-05
New Economics Papers: this item is included in nep-sea
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