The Research Of The Black-Scholes Option Pricing Model Under The Situation Of Dynamic Investment Strategy

Option is an example of financial derivative's innovation. Option is an important tool for investors to keep away risk. The formula of Black-Scholes analyzes the pricing of option and risk management from the quantitative view. This is a powerful sustainment for the option's popularization. Traditional Black-Scholes formula hasn't considered the investors'behavior under the situation that the price of stock changes. Black-Scholes formula only assumes that investors keep away risk using option, neglects that the investors can keep away risk and reduce risk through buying and selling stocks. If we consider this in the course of option pricing, the lost of buying stocks that option must redeem is smaller than not buying stocks.This paper considered the investors'behavior of keeping away risk and the Investment strategy of reducing the lost when build the model of option pricing. These improvements are on the basis of traditional Black-Scholes formula. Using the relative theory on Black-Scholes option pricing, we get the call option and put option's pricing formula under the situation of dynamic investment strategy. Also we get the formula's property through analyzing its all aspects. At last, we compare our formula with traditional formula and get the result that option price under dynamic investment strategy is lower than the price made by Black-Scholes formula when keeping away the same risk.