EGARCH Option Pricing with Assymetries in the Mean Equation

Black's option pricing model systematically misprices actual option premiums. The biases of Black's model may result from assuming non-stochastic volatility and normality. A generalized autoregressive conditional heteracedastic(GARCH) option pricing model relaxes the assumptions of Black's model This paper uses an asymmetric ARCH-type models. Among ARCH-type alternatives; the asymmetric EGARCH(0,1)-t model fits Chicago wheat futures prices better than several alternative ARCH-type models. A Monte Carlo study shows that Black's model underprices deep out-of-the-money put options relative to the EGARCH option pricing model when the true underlying process Is an EGARCH process Differences between Black's model and the EGARCH option pricing model increase as time to maturity increases. When used to forecast actual option premiums of Chicago wheat futures contracts, the mean squared errors of the EGARCH option pricing model with deep in-the-money put and call options and with deep out-of-the-money put options are significantly smaller than thaw of Black's model.