Option Pricing Under Stochastic Interest Rates:an Empirical Investigation

The classic Black-Scholes model plays a vital role in the development of option pricing. In the basis of the constant risk-free rate and some other special hypothesis, the European option pricing formula(the B-S formula) was obtained by Black and Scholes. However, there are some errors between market price and the option price calculated by the B-S formula. Many scholars have paid more and more attention to the issue of pricing error. Considering the interest rate changes frequently, some scholars have proposed stochastic interest rate models and have studied the option pricing under such models.This paper studies the effect of stochastic interest rate on option pricing by empirical analysis. We choose the S&P500 index options as the object of the research. After making statistical analysis for the option pricing models under the four kinds of stochastic interest rate(MHL, Vas, CIR and BrS) through the historical data, we got the empirical results about the influence of stochastic interest rate on option pricing. Firstly, we discretized the four stochastic interest rate models and estimated the parameters of stochastic interest rate models using the historical data of overnight call money rate and the S&P500 index. Then we compared the pricing errors of option pricing models under the four kinds of stochastic interest rate and the Black- Scholes model. In the meaning of the average relative error, it shows that for the S&P500 index call options, neither a specific stochastic interest rate model is always more accurate than another stochastic interest rate model, nor a specific stochastic interest rate model is always more accurate than the Black-Scholes model. However, for the out-of-the-money options, or the at-the-money options with short or medium term, using the MHL model is more accurate. While for the in-the-money options, using the Vas model is more accurate.