Valuation of NDX Index Call Options with Fractional Black-Scholes Model

This study compares the accuracy between the fractional Black-Scholes (FBS) option pricing model and the Black-Scholes (B-S) option pricing model using NASDAQ-100 (NDX) index call options data for the period of four years from January 2004 to December 2007. The degree of accuracy is measured by moneyness, variance estimate, and maturity. Although the accuracy of the FBS model is sensitive to Hurst parameter (H), the parameter is not directly observed. We recover the H value from the FBS model which depends on variance estimates. Because the FBS model has two unknown parameters, volatility and the Hurst parameter, we propose model predicting option prices to estimate H values using the implied volatility. We find that the FBS model outperforms the B-S model across the board. In particular, there is a great advantage of using the FBS model with historical volatility.