Research On Option Pricing

Evading risk in financial trading market cries for pricing options to a nicety.On the base of the B-S's pricing formula of European option,we obtain the common option pricing method.And we introduce the contents methods and results about the pricing theory of option.Assuming that there is no arbitrage and there are two securities traded one of which is riskless and the other is risky in the efficiency market.in this article.We will give several new means of proof on several options' pricing in different model of stock. 1. Research on standard European optin pricing :We obtain the BSDE option price satisfies by self-financing strategy,and we will get the probability expression formula of European options' price;then we will give the proof of the complete hedging of European option. 2.Research on American options pricing: Researching American option usually study its pricing and optimal exercise moment.Inthis article,we consider the optimal stopping problem related to { U(Sn)/(1+r)n} and U(ST)/ert ,i.e,when to maximize the utility of American options in the market which is discrete continuous and efficient.On the other hand U{x) is utility function based on stock price.