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

TL;DR

This paper develops approximate closed-form pricing formulas for arithmetic Asian options under a mixed fractional Brownian motion model, incorporating jumps, to better capture long-range dependence and self-similarity in financial markets.

Contribution

It introduces analytical pricing formulas for Asian options under mixed fractional Brownian motion with jumps, extending existing models to include jump processes.

Findings

Derived approximate closed-form solutions for Asian options.

Incorporated jumps into the mixed fractional Brownian motion model.

Provided analytical formulas based on strike price approximation.

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.