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.