Modification Of Black-Scholes Option Pricing Model

The theory and practice of derivative securities have undergone rapid development in the last twenty years all over the world. Many mathematicians and financial economists pay more and more attention to the problems of option pricing. Pricing options is the focus of option transactions, because transactions carry on through comparing the real market prices with the true option values. Among all the derivative pricing systems, the research of option pricing is the most extensive. In 1973, American financial economists, Black and Scholes, proposed the famous Black-Scholes Model of option pricing under the suppositions that there exists an effective market, that the stock price abides by geometric Brownian motion and that the expectant payoff and volatility of stock is constant. The Black-Scholes Model is in fact an ideal state, for some of its suppositions can't be met in the real market. Based on the supposition to change the Black-Scholes Model, this paper proposed some improved models and pricing formulas, which will make stock price more close to the operating rules of real market and therefore more practical in option pricing.What this paper deals with is as follows:(1) Firstly based on the analysis of the current situation and foreground of the theory about option pricing, explain the Black-Scholes Model of option pricing and give a new way to pricing option formulas with the theory of martingale.(2) On the instance that the model is jump-diffusion, and that the stochastic interest rate is stochastic, derivative some new option pricing formulas.