European Option And American Option Pricing Numerical Method To Further Study

On the base of the non-arbitrage principle and the risk neutral valuation, we discuss European option and American option pricing. The main wok includes the following contents.(1) Analyze relevant theories and methods of European option pricing;(2) Investigate numerical methods of American option pricing, and improve precise valuation via new parameters;(3) Study the fair price of European option and optimal time of American option through the hedging method based on G-hedging.First, we get European option pricing formula by Black-Scholes model, and several numerical methods of derivative valuation in incomplete markets are discussed and compared. Then, we mainly deal with the binomial tree method and the finite difference method for American option pricing. The binomial tree parameter model has the flaw, for instance, it will have the negative probability in some kind of situation. So we construct new binomial tree parameter model, which will never have the negative probability and have the very high computation precision with the aid of the thought of the random error. Thus it might be applied to kinds of American put option pricing; moreover the new model might be extended to the trinomial tree and the higher order trees. In the finite difference method, we adopt control variable technique to obtain precise valuation.At last, we discuss European option and American option pricing based on G- hedging, and prove optimal hedging-time of American option is a stopping-time.