Abstract
In this article, we mainly estimate the parameters of GARCH (1,1) model to simulate the index prices and use jump diffusion process to simulate the interest rate paths in the stochastic interest rate model. Therefore, we release the assumption in Black-Scholes model that the volatility and interest rate are taken unchangeable. On the other hand, because the fixed-income securities in Taiwan are not as popular as other advanced countries, our interest rate will be smooth and steady after a jump occurrs. Moreover, in our result, the volatility of interest rate in Taiwan is estimated nearly zero.To conclusion, when comparing with the market price, we find that the model combining GARCH (1, 1) model and CIR model with jump diffusion process could get better performance than single GARCH (1,1 ) model and Black-Scholes model.