Implied Volatilities of S&P 100 Index with Applications to Financial Market

Abstract

This paper studies the implied volatilities of the S &P 100 from the prices of the American put options written on the same index. The computations are based on a recursive Binomial algorithm with prescribed error tolerance. The results show that the volatility smile exists, thus the classic Black-Scholes’s approach of using a constant volatility for pricing options with different trading conditions is not plausible. The method discussed in this work contrasts the likelihood ratio method contained in [6]. Further studies with expanded data set are recommended for comparing the effectiveness of these two methods in forecasting stock market shocks.