Volatility Measurement, Modeling and Forecasting—An Overview of the Literature

The paper presents an overview of the literature on volatility measurement, modeling and forecasting, from the perspective of option pricing. The following conclusions are drawn. First, efficient volatility estimation utilizes intraday data and measures such as realized volatility (i.e. sum of squared returns calculated over short, e.g. 5-minute, time intervals) or realized range. Second, volatility lends itself—at least to some extent—to forecasting, whereby the most efficient forecasts are those extracted from option prices quoted on the market, which squares with the basic theory of forecasting as market expectations are based on a broader set of information than backward-looking time series forecasts. Third, although Black-Scholes option pricing theory was derived under the assumption of constant volatility, the approach can be fairly easily generalized to cover cases of time-dependent, time and asset price dependent, and even stochastic volatility. Each of those models allows to capture some key element of the empirically observed pattern of market returns and each allows constructing a hedged option position that leads to a differential equation determining the option price (under specified boundary conditions), although not always in closed form.