A Study on Black-Scholes Model and Implied Volatility

[[abstract]]Black-Scholes Model, a famous options pricing theory, has been widely used to evaluate the price of financial derivatives. Despite of the fact that many scholars argued against the model and attempted to modify it, Black-Scholes Model, now an academic research focus, remained the basis of all improved models. After reviewing the previous literature, the researcher found that only a small number of studies had elaborated the meaning of the pricing theory. Ever since 1973, the researcher hasn?t found any paper in which the formula for call price and put price of European style options was systematically derived. The purpose of this thesis is to derive the formula through reviewing Fisher Black and Myron Scholes? theory and then to describe the model in detail. Second, the researcher attempted to elaborate the meaning of the pricing theory from the aspects of physics and statistics. Third, the researcher adopted a simple formula to quickly calculate the implied volatility. In addition, the researcher introduced the Newton?s method to accurately calculate the implied volatility. Based on implied volatility, we can calculate the value of pricing sensitivities for hedging and try to figure out the optimal investment policy. Finally, the researcher has found out an investment policy for arbitrage by using high volatility spread with low risk. The empirical results on TAIEX Options Market indicated that there have been many opportunities for arbitrages by using this policy and investors could thus have better chances to enjoy a high profit rate. The study would provide some guidelines to investors about TXO options and to the beginners studying B-S Model