The evaluation of geometric Asian power options under time changed mixed fractional Brownian motion

TL;DR

This paper develops a new pricing formula for geometric Asian power options using a time-changed mixed fractional Brownian motion model, extending traditional models to account for complex stochastic behaviors in stock prices.

Contribution

It introduces a novel mixed fractional subdiffusive Black-Scholes model and derives explicit pricing formulas for Asian power options under this framework.

Findings

Derived a pricing formula for geometric Asian options with fractional dynamics.

Provided lower bounds and special case analyses for Asian options.

Applied the model to price dividend-paying stocks with power payoffs.

Abstract

The aim of this paper is to evaluate geometric Asian option by a mixed fractional subdiffusive Black-Scholes model. We derive a pricing formula for geometric Asian option when the underlying stock follows a time changed mixed fractional Brownian motion. We then apply the results to price Asian power options on the stocks that pay constant dividends when the payoff is a power function. Finally, lower bound of Asian options and some special cases are provided.