Generalization About The B-S Model And The Stock Price Model With Lévy Type

In option pricing, the celebrated B-S formula was given in complete market when both the riskless rate and the volatility are constants.But in the real world, the riskless rate is usually stochastic.So this paper generalized the B-S model when the riskless rate was stochastic in chapter 3,and gave the related option pricing formula.In B-S model,the stock price process is driven by Brown motion. We know, the change of stock price is influenced by many factors, particularly the great events.So the more reasonable assumption is one that allows jumps.In chapter 4 of this paper, we looked back the classic jump-diffusion model ,and studied the stock price model with stochastic volatility ,proved that there existed probability measure under which,the discounted stock price process was a martingale.