European option pricing problem based on a class of Caputo-Hadamard uncertain fractional differential equation

Abstract

Uncertain fractional differential equation (UFDE) is very suitable for describing the dynamic change in uncertain environments. In this paper, we consider the European option pricing problem by applying the Caputo-Hadamard UFDEs to simulate the dynamic change of stock price. First, an uncertain stock model with the mean-reverting process is studied, and the European option pricing formulas are given. Then, the effect of uncertain interference on the bond is considered, and the corresponding European option pricing formulas are presented. Finally, some numerical examples are given to illustrate the effectiveness of pricing formulas.

Keywords

• uncertainty theory
• uncertain fractional differential equation
• mean-reverting process
• european option
• uncertain interference