In the early 1980s, R.F. Engle pioneered the econometric technique of Auto-Regressive Conditional Heteroskedasticity (ARCH), which has subsequently generated a very considerable literature. This collection brings together the leading papers which have shaped ARCH research from its inception to the latest developments. Papers present both theory and financial market analysis, and discuss the key issues in the use of ARCH models to study volatility and correlation: - what model to use - what time intervals to employ - how to model multivariate systems - how to apply the models to price and trade options - how to model volatility spillovers across markets and within the day For each of these issues, the selection of a number of papers by different authors allows a variety of viewpoints to emerge. Many applications to financial markets are included, and a new introduction by the editor connects the papers to trace the development of the field. the result is a timely, useful book which will bring graduate students, faculty, and practitioners up to date on this rapidly expanding field of research.