Stochastic volatility (SV) is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. In this book I bring together some of the main papers which have influenced the field of the econometrics of stochastic volatility with the hope that this will allow students and scholars to place this literature in a wider context. We will see that the development of this subject has been highly multi- disciplinary, with results drawn from financial economics, probability theory and econometrics, blending to produce methods and models which have aided our understanding of the realistic pricing of options, efficient asset allocation and accurate risk assessment.
Time-varying volatility and codependence is endemic in financial markets. Only for very low frequency data, such as monthly or yearly asset returns, do these effects tend to take a back seat and the assumption of homogeneity seems not to be entirely unreasonable. This has been known for a long time, early comments include Mandelbrot (1963), Fama (1965) and Officer (1973). It was also clear to the founding fathers of modern continuous time finance that homogeneity was an unrealistic if convenient simplification, e.g. Black and Scholes (1972, p. 416) wrote ‘‘...there is evidence of non-stationarity in the variance. More work must be done to predict variances using the information available.’’ Heterogeneity has deep implications for the theory and practice of financial economics and econometrics.