Option Pricing With Volatility Of Stock Price And An Empirical Research

The stock option is an option to buy a certain quantity of a stock for current price within a specified time in the future. Holder of option may exercise or abstain. Because the stock option has scheduled risk which doesn't exceed the fee of the option paid by the buyer of option, the risk is limited that is beneficial to keep the financial market prosper and stable. But because the stock option is a kind of commodity in the financial market, the mathematical model of the stock option about the priced problem is very important. In the pricing of the stock option, the influence factor is current price of stock, strike price, stock price for the maturity date of the option contract, rate with no risk, fluctuate rate of stock price, due time. The classic model about the pricing of the stock option is B-S formula and its rigidity in mathematics is beneficial to calculating, but its hypothesis of the perfect market and that fluctuate rate is fixed and unchanged doesn't agree with the practical market, so the theoretical field are all along engaged in improving the calculating model of the stock option. Along with more and more complicated random circumstance appears, the demand in theory is especially evident.This paper will study concrete numeric algorithm, explain the calculating method of the fluctuate rate and make demonstration analysis and match the influence of the fluctuate rate of the stock price on the pricing of the stock option according to the B-S model and the GARCH(1,1) model.