基于混合分数布朗运动下带跳的两值期权定价

Binary Option Pricing with Jump Based on Mixed Fractional Brownian Motion

本文研究了股票价格服从混合分数布朗运动模型下带跳过程的两值期权的定价问题。首先通过热传导方程理论得到了两值期权的定价公式,随后用保险精算方法得到了两值期权的级数解公式,然后应用蒙特卡洛模拟的方法和有限差分方法得到数值解。以热传导方程得到的定价公式作为标准,将其余三种方法得到的期权价格与定价公式解进行比较,通过比较的结果,得出了这种级数解和数值方法的可行性和有效性。

In this paper,we study the pricing problem of binary options in which stock price obeys the mixed fraction Brownian motion model with jump.First,the pricing formula of binary options is obtained through the heat conduction equation theory,and then the series solution formula of binary options is obtained by the insurance actuarial method.Then,the numerical solution is obtained by means of Monte Carlo simulation and finite difference method.Using the pricing formula obtained by the heat conduction equation as the standard,the options price obtained by the other three methods is compared with the pricing formula solution,and the results are compared.The feasibility and validity of this method are obtained.