利率服从Vasicek模型下的欧式期权定价

European Option Pricing under the Vasicek Model of the Interest Rate

本文提供一种随机利率模型下的欧式期权定价的解析解。首先对不支付红利的零息票债券进行定价,提高其精度。然后利用股票、债券、期权进行投资组合得到欧式期权满足的随机微分方程,并通过变换得到它的显式解。最后通过数值试验验证其有效性,同时分析了随机利率对欧式看涨期权的影响。

Base on the stochastic nature of the rate,an explicit option pricing formula is obtained for European option.First of all,we derive the pricing formula for a riskless zero-coupon bond under the Vasicek mordel to enhance its accuracy,then we form a hedge portfolio consisting of the stock,the riskless bond,and the call to derive a stochastic differential equation,and solve its explicit solution.A numerical example is given for verifying the validity of the formula,and analyzing the effects of stochastic interest rate for European option pricing.