The Research Of The Volatilities Estimation Based On Copula Functions

In the classical Black-Scholes’s formula, the underlying asset’s volatility is the only variable which can’t be observed directly. Thus, the estimation of volatility plays a very important role in option pricing. The finance circles usually use implied volatilities of the at-the-time options as the real ones which has a big deviation with the reality. To make it closer to the market, we have made a deep research of stocks’volatilities in the frictional financial market which considers the transaction costs. We also take the dividends into consideration on the base of classical B-S. With the theories and methods of Copula, we make an empirical analysis of S&P500to compare the estimation of implied volatilities of at-the-time options and the ones with the highest Vega. We prove that implied volatilities of the ones with the highest Vega is doing better.