Introduction

Abstract

Measurement of the volatility/covariance of financial-asset returns plays a central role in many issues in finance, e.g., risk and investment management, hedging strategies, forecasting. In connection with financial markets the word volatility is usually associated with the concepts of risk and opportunity, thus referring to a measure (as well as a feeling) of the movements and uncertainty in the markets. As a matter of fact, the constant-volatility assumption prescribed by the Black & Scholes model (Black and Scholes (1973)) does not account for some stylized facts such as variance heteroscedasticity, predictability, volatility smile, covariance between asset returns and volatility (the so-called leverage effect). Therefore, a wide set of time-dependent (stochastic) volatility models have been proposed to model asset-price evolution and to price options coherently with this evidence. Nevertheless, the volatility process is unobservable and its latency leads to the difficult task of developing efficient methods to measure it.

Labitur occulte fallitque volatilis aetas (Ovidio, Metamorfosi, Liber X v. 519–520)