European Option Pricing under the Vasicek Model of the Interest Rate

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.