A GARCH model of the implied volatility of the Swiss Market Index from options prices

This paper estimates the implied stochastic process of the volatility of the Swiss market index (SMI) from the prices of options written on it. A GARCH(1,1) model is shown to be a good parameterization of the process. Then, using the GARCH option pricing model of Duan (1991), the implied volatility process is estimated by a simulation minimization method from option price data. We find the persistence of volatility shocks implied by options on the SMI to be very close to that estimated from historical data on the index itself. Comparing the performances of the implied GARCH option pricing model to that of the Black and Scholes model it appears that the overall pricing performance of the former is superior. However the large sample standard deviations of the out-of-sample pricing errors suggest that this result should be taken with caution.