Pricing Problem of Geometric Average Asian Barrier Option Based on Uncertain Fractional Differential Equation

Abstract

In this paper, we investigate pricing problems of geometric average Asian barrier options based on a Caputo type of uncertain fractional differential equation. Unlike traditional stock models based on stochastic/ uncertain processes, we assume that underlying assets are subject to uncertain fractional processes. First, it provides a Caputo type of uncertain fractional mean-reverting model based on fractional differential equation. Then the pricing formulas are acquired for four geometric average Asian barrier options, namely, the up-and-in call option, the down-and-in put option, the up-and-out put option and the down-and-out call option. Meanwhile, numerical simulations are devised to validate the results of the model.