An Empirical Analysis Of Option Pricing Under Stochastic Interest

The1970s Black-Scholes model plays a great impact on the development of the European option pricing model, Black-Scholes model considerations little and easy to get, which is widely used. However, the model has its limitations, it is considered interest rate is fixed, the cvolatility of interest rates is not consistent with the actual situation, therefore, the model will be difficult to avoid the resulting pricing errors. To compensate for this deficiency, many scholars began to study the option pricing under the random fluctuations in interest rates, creative developed a variety of stochastic interest rate models. Merton-Ho-Lee Interest rate model (1973), and in1977Vasicek exported the Vasicek interest rate model, option pricing under stochastic interest rates had a significant impact.In this paper, the Vasicek interest rate model and MHL interest rate model pricing in the medium-term and short-term S&P500index call options, observe the pricing error, and compare with the pricing error of the Black-Scholes model. First, build a model, and then estimate all the parameters of the model, and finally obtained the pricing results and the corresponding pricing error. Empirical Analysis Conclusions:(1)under the Black-Scholes model in the medium-term and short-term index call option pricing errors smaller than in the short-term Vasicek interest rate model index call option pricing error, under the MHL model in the medium-term and short-term index call option pricing errors smaller than in the short-term Black-Scholes interest rate model index call option pricing error;(2) Vasicek interest rate models, MHL interest rate models for short-term index call option pricing errors smaller than the medium-term index call option pricing error, and the Black-Scholes model as well.