Research On The Black-Scholes Stock Option Pricing Model Based On Special 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. So the risk of option's saller may be very large.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, so it may have larger interesting for the investor.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 using the partial differential equation and the financial energy theory and using demonstration . 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.Through a large amount of theories deriving and empirical researches, this paper reaches the following conclusions: (1) Through theory deriving, get the Black-Scholes call stock option pricing model based on dynamic investment strategy; setting different linear investment strategy parameter and the upper limit of the investment percentage, analyzing the differ between the classical option and the new call option; (2) Through theory deriving, get the Black-Scholes put stock option pricing model based on dynamic investment strategy; setting different linear investment strategy parameter and the least percentage of the stock held, analyzing the differ between the classical put option and the new put option; (3) Deriving the Black-Scholes stock call option model based on discrete investment strategy and analyzing the sensitivity of the new call option. Setting different linear investment strategy parameter and the upper limit of the investment percentage, analyzing the differ between the classical option and the new call option; (4) Deriving the Black-Scholes stock put option model based on discrete investment strategy and analyzing the sensitivity of the new put option. Setting different linear investment strategy parameter and the least percentage of the stock held, analyzing the differ between the classical put option and the new put option; (5) Expatiation the application principle of the investment strategy, and combine the data from the HKEx(Hong Kong Exchanges and Clearing Limited) get empirical researches, analyzing how to carry on the investment strategy in real environment.During the research of this paper, the author try to take advantage of the existed outcomes, thoroughly extracts the rational elements of financial innovation Theory, Investment Theory. This paper has created the new theoretical framework and approach of the Black-Scholes stock option pricing model based on investment strategy, and devised the option pricing model based on discrete investment strategy. It makes the paper innovative and instructive both in theory and in practice.