An Empirical Study For Implied Volatility Measure Of S&P500Index Options

An important premise of the original B-S model is that the volatility of underlying asset price is constant relative to the exercise price. But in fact, volatility changes as exercise price, especially for the deep in-the-money and out-the-money options, which is the observed phenomenon of "volatility smile". The volatility smile phenomenon makes it unclear which implied volatility provides the best measure of the market volatility expectation over the remaining life of the option. Due to the high liquidity of at-the-money option and the low sensitivity of its implied volatility to the price error, the at-the-money implied volatility is often considered a good measure of future volatility. In this paper, we raise the question:is at-the-money implied volatility the best we can do? We provide in this paper an analytical rationale that the implied volatility from option with highest Vega outperforms the at-the-money implied volatility in terms of forecasting ability, especially for long forecasting horizons. We analyse the S&P500index call option and get conclusion that Our empirical findings are consistent with our theoretical argument. Based on our theoretical argument and our empirical results, in practice, we suggest that implied volatilities from frequently traded out of the money but near the money options (highest Vega option) be used to estimate future volatility of the underlying asset. It provides some suggestions and theoretical basis for investment decision and risk management.