Pomiar i modelowanie zmienności — przegląd literatury

The paper presents an overview of the literature on volatility measurment, modeling and forecasting, from the perspective of option pricing. The following conclusion are drawn. First, efficiency volatility estimation utilizes intraday data and measurmes 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, where by the most efficient forecasts are those extracted from option prices quoted on the marked, which squares with the basic theory of forecasting as market expectations are based on broader set of information than backward-looking time series forecasts. Third, althought Black-Scholes opinion pricing theory was derived under the assumption of constant volatility, the approach can be fairly easily generalised to cover cases of time demendent, 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 boundry conditions), although not always in closed form.