Volatility ranks among the most active and successful areas of research in econometrics and empirical asset pricing finance over the past three decades. This research review studies and analyses some of the most influential published works from this burgeoning literature, both classic and contemporary. Topics covered include GARCH, stochastic and multivariate volatility models as well as forecasting, evaluation and high-frequency data. This insightful review presents and discusses the most important milestones and contributions that helped pave the way to today's understanding of volatility.

We find that the difference between implied and realized variances, or the variance risk premium, is able to explain more than fifteen percent of the ex-post time series variation in quarterly excess returns on the market portfolio over the 1990 to 2005 sample period, with high (low) premia predicting high (low) future returns. The magnitude of the return predictability of the variance risk premium easily dominates that afforded by standard predictor variables like the P/E ratio, the dividend yield, the default spread, and the consumption-wealth ratio (CAY). Moreover, combining the variance risk premium with the P/E ratio results in an R DEGREES2 for the quarterly returns of more than twenty-five percent. The results depend crucially on the use of "model-free," as opposed to standard Black-Scholes, implied variances, and realized variances constructed from high-frequency intraday, as opposed to daily, data. Our findings suggest that temporal variation in risk and risk-aversion both play an important role in determining stock market returns.

Recent empirical evidence suggests that the variance risk premium, or the difference between risk-neutral and statistical expectations of the future return variation, predicts aggregate stock market returns, with the predictability especially strong at the 2-4 month horizons. We provide extensive Monte Carlo simulation evidence that statistical finite sample biases in the overlapping return regressions underlying these findings can not explain" this apparent predictability. Further corroborating the existing empirical evidence, we show that the patterns in the predictability across different return horizons estimated from country specific regressions for France, Germany, Japan, Switzerland and the U.K. are remarkably similar to the pattern previously documented for the U.S. Defining a global" variance risk premium, we uncover even stronger predictability and almost identical cross-country patterns through the use of panel regressions that effectively restrict the compensation for world-wide variance risk to be the same across countries. Our findings are broadly consistent with the implications from a stylized two-country general equilibrium model explicitly incorporating the effects of world-wide time-varying economic uncertainty.

Robert Engle received the Nobel Prize for Economics in 2003 for his work in time series econometrics. This book contains 16 original research contributions by some the leading academic researchers in the fields of time series econometrics, forecasting, volatility modelling, financial econometrics and urban economics, along with historical perspectives related to field of time series econometrics more generally.
Engle's Nobel Prize citation focuses on his path-breaking work on autoregressive conditional heteroskedasticity (ARCH) and the profound effect that this work has had on the field of financial econometrics. Several of the chapters focus on conditional heteroskedasticity, and develop the ideas of Engle's Nobel Prize winning work. Engle's work has had its most profound effect on the modelling of financial variables and several of the chapters use newly developed time series methods to study the behavior of financial variables. Each of the 16 chapters may be read in isolation, but they all importantly build on and relate to the seminal work by Nobel Laureate Robert F. Engle.
About the Series
Advanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.