Option Implied Volatility

The volatility smile phenomenon appears to violate the Black-Scholes model and has puzzled numerous scholars. This book uses the relation between the option vega and its moneyness to rigorously demonstrate that the price error alone can produce a smile phenomenon even if the Black-Scholes model is correct. The smile phenomenon makes it unclear which implied volatility provides the best measure of the market volatility expectation over the remaining life of the options. Due to the high liquidity of the at-the-money option and the less sensitivity of its implied volatility to the price error, the at-the-money implied volatility is often considered a good measure of the future volatility. This book raises the conjecture that the implied volatility from the option with the highest vega outperforms the at-the-money implied volatility in terms of the forecasting ability, especially for long forecasting horizons, due to the even higher liquidity of the option with the highest vega and the least sensitivity of its implied volatility to the price error. Empirical testing results are consistent with this conjecture.

Guan Jun Wang received her PhDs in Stochastic Control from the Chinese Academy of Sciences and Finance from Syracuse University. She was an Associate Professor of Mathematics at the Central University for Nationalities in China prior to her coming to the USA. Since August 2007, she has been teaching at Florida A & M University as a visiting assistant professor of finance. Her primary research interests lie in mathematical finance including volatility modeling and forecasting, derivatives pricing and default bond valuation. She has published in journals such as SIAM Journal of Applied Mathematics and IEEE Transactions on Automatic Control.