Investigating the information content of the model-free volatility expectation by Monte Carlo methods

We explore the impact of both the number of option prices and the measurement errors in option prices upon the information content of the model-free volatility expectation, and compare it with the Black–Scholes at-the-money (ATM) implied volatility. We simulate the realized volatility process and option prices using Heston\u27s price dynamics and option valuation formula. The results show that the model-free volatility expectation always contains important information about future realized volatilities. When the option prices contain random measurement noise, the informational efficiency of the model-free volatility expectation increases monotonically with the number of out-of-the-money options. The model-free volatility expectation outperforms the ATM implied volatility, except when there are only a few option price observations. For the traded strikes for S&P 500 index options, we further show that fitting implied volatility curves before applying the current CBOE procedure for constructing the VIX index can improve the VIX\u27s efficiency when forecasting future realized volatilities