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

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  • Foad Shokrollahi
  • Davood Ahmadian
  • Luca Vincenzo Ballestra

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.

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  • Foad Shokrollahi & Davood Ahmadian & Luca Vincenzo Ballestra, 2021. "Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps," Papers 2105.06999, arXiv.org.
    • Handle: RePEc:arx:papers:2105.06999
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    References listed on IDEAS

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