Certain Option Pricing Formulas Under Stochastic Interest Rate

In this paper, under the stochastic interest rate, we got the pricing formula of standard European call option by means of measure transformation. Then using Ito's lemma, equivalent martingale measure and Girsanov theorem, when interest rates were subject to Ornstein-Uhlenbeck model, we had obtained a linear segment options' pricing formula, in which the linear segment options' pricing formula was:Theorem A. Setting the option expiry date T, when the stock exercise price K could satisfy K∈[x1,x2] under the condition at time T, the option price provided for a+bST. Then when the interest rates met the drt= (θt-atrt)dt+σr(t)dZt, linear Interval option pricing formula at time t was as follows:Where,And finally by the same way, we obtained the standard European-style hat call options, the standard European two-style call options and standard European gap call options, from this article in the interest rate subject to the same interest rate model, and generalize the conclusions of previous articles.