IMPLIED ARCH MODELS FROM OPTIONS PRICES

This paper estimates the implied stochastic process of the volatility of an asset from the prices of options written on the asset. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is used to parameterize the process. Then the GARCH model implied by the option market is estimated by a generalized simulation minimization method from option price data. The persistence of volatility shocks implied by options on the Standard & Poor's 500 is found to be similar to that estimated from historical data on the index itself. However, the implied persistence after the meltdown in October 19, 1987 was much weaker. We use post October 19, 1987 data on the cash market prices to verify the correctness of the option markets' use of the less persistent model.