混合分数布朗运动下有交易成本和红利支付的两值期权定价

Pricing of Binary Options with Transaction Costs and Dividends Driven by Mixed Fractional Brownian Motion

本文首先建立考虑交易费用和红利支付的标的资产服从几何混合分数布朗运动的两值期权定价模型.然后利用Mellin变换,得到两值期权的定价公式,进而得到所建模型的欧式期权定价公式.最后通过数值模拟,分析本文定价模型中标的资产价格、Hurst指数、交易费用比率、波动率等参数对两值期权价值的影响.

In this paper a pricing model to a binary option with transaction costs and dividends is established,where the stock price follows a geometric mixed fractional Brownian motion.Then by applying the Mellin transform a pricing formula of binary options is given and furthermore,the pricing formula of European options to our model is obtained.Finally,numerical simulations are carried out to illustrate the influences of the asset price,Hurst index,transaction costs ratio,volatility and other parameters on the value of binary options.