GARCH option pricing with implied volatility

Abstract

Generalized autoregressive conditional heteroskedasticity (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. This paper estimates implied volatilities from GARCH OPM. The estimated implied volatilities are used to forecast option premia. The GARCH OPM with implied volatility provided more accurate estimates of option premia than the Black option pricing model with implied volatility for options ranging from six to sixteen days to maturity. For options ranging from 21 to 50 days to maturity the Black OPM with implied volatility was more accurate than the GARCH OPM with implied volatility.