Geometric Asian option pricing under the environment of a mixed fractional Brownian motion and discrete dividend payments

Abstract

In this paper, the price process for underlying assets is modeled as a mixed fractional Brownian motion (MFBM) to account for the long memory in financial markets and remove arbitrage opportunities. Furthermore, the issue of the behaviors of price options with known discrete cash dividends on the underlying asset is taken into account. This study addresses the pricing issue of knowing dividends by rewriting the equation for the price movement of the underlying asset using the MFBM model. The pricing expression for geometric Asian options in the context of MFBM, with discrete dividend payouts, is proposed and derived in this work. Then numerical experiments have been conducted on the crucial parameters within the expression, wherein an analysis of the impacts of parameter variations on the prices of geometric Asian options has been also carried out. Subsequently, empirical analyses are undertaken to compare our model with option prices under continuous dividend payments, elucidating the effectiveness and practicality of this model.