Long-Memory versus Option-Implied Volatility Predictions

Abstract

Volatility is a critical parameter in virtually all option pricing models. But the closer we look at volatility, the harder it seems to be to model it correctly. The constant volatility assumption of early pricing models is clearly inadequate. GARCH family models make volatility a function of the asset price process, and stochastic volatility models bring in a second stochastic factor that affects volatility movements. These approaches make sense in theory, but empirically volatility shocks seem to be too persistent to be consistent with them. A further confounding factor is that implied volatilities extracted from option prices in the market are widely thought to give more accurate predictions of future realized volatility, but don't obey any of these models exactly. In this article, Li examines a volatility model with “long memory,” meaning that it can be made to fit the slow-decay feature of market volatilities. He also introduces a much more extensive data series, with intraday observations every five minutes. Using such a dense price series, realized volatility becomes observable, and the vast number of data points allows precise estimation of model parameters. For exchange rates on the deutsche mark, the yen and the British pound, the ARFIMA (“Autoregressive Fractionally Integrated Moving Average”) model is shown to give a better fit to volatility behavior than the alternative model, and it beats implied volatility substantially in the standard tests of forecasting performance.