随机利率分数布朗运动模型下的欧式双向期权定价

Pricing of Bi-direction European Option Under Fractional Brownion Motion with Stochastic Interest Rates

在经典的期权定价模型中,假设股票价格服从标准几何布朗运动,但金融实证表明用分数布朗运动描述股票价格过程更贴近市场.假设标的资产服从几何分数布朗运动,无风险利率r(t)服从Vasicek扩展模型,红利率q(t),波动率σ(t)为随时间变化的确定函数,运用拟鞅及测度变换的方法求出了欧式双向期权的定价公式.

In the classical option pricing model stock price was supposed to follow standard geometric Brownian motion. However financial evidence shows that using fractional Brownian motion to describe the process of stock price is more closer to the market. In this paper, we assume that underlying asset price fol- lows geometric fractional Brownian motion,the riskless rate r（t） follows Vasicek extended model,dividend rate q（t）,and the volatility a（t） of the stock are all time-varying certain functions. By the help of quasi- martingale and change of measure, we get the pricing formulas of bi-direction European option.