Garch Option Pricing with Implied Volatility

Generalized autoregressive conditional heteroskedasticity (GARCH) provides a better ft to futures price data than the common assumption of identical independent normal distribution. GARCH option pricing models (OPM) with historical volatility have proven superior to the log-normality assumption of the Black option pricing model with historical volatility. Implied volatilities derived from GARCH OPM might therefore be expected to provide better guidance in investment decisions than those derived from the Black option pricing model. This paper estimates implied volatilities from GARCH OPM. The estimated implied volatilities are used to forecast option premia. Results are compared against forecasts of option premia using implied volatilities from Black's option pricing model. The GARCH implied volatilities are more stable than the Black implied volatilities. The GARCH option pricing model with implied volatility outperformed the Black option pricing model with implied volatility in terms of forecasting actual option premia.