Abstract

This essay collection focuses on the relationship between continuous time models and Autoregressive Conditionally Heteroskedastic (ARCH) models and applications. For the first time, Modelling Stock Market Volatility provides new insights about the links between these two models and new work on practical estimation methods for continuous time models. Featuring the pioneering scholarship of Daniel Nelson, the text presents research about the discrete time model, continuous time limits and optimal filtering of ARCH models, and the specification and estimation of continuous time processes. This work will lead to a rapid growth in their empirical application as they are increasingly subjected to routine specification testing.

• Provides for the first time new insights on the links between continuous time and ARCH models
• Collects seminal scholarship by some of the most renowned researchers in finance and econometrics
• Captures complex arguments underlying the approximation and proper statistical modelling of continuous time volatility dynamics

"Finance applications have led to a rebirth of interest in continuous time econometric modelling. This volume stresses the achievements of Dan Nelson and includes important contributions." --PETER M. ROBINSON, London School of Economics

"This volume contains some important contributions to a young but burgeoning literature and is a worthy tribute to Dan Nelson's research. Continuous-time econometrics has finally arrived!" --ANDREW W. LO, Harris & Harris Group Professor, MIT Sloan School of Management, Cambridge, Massachusetts.

"This volume provides much practical guidance for implementing continuous-time models using real-world data, recorded in discrete time. The articles offer methods and insignts relevant to modelling and estimating volatility in the stock market as well as other financial markets, such as fixed income and foreign exchange." --ROBERT F. STAMBAUGH, University of Pennsylvania

"This collection of path-breaking papers contains useful insights for a range of readers. For financial economists and others interested in modelling the behavior of volatility over time, Daniel Nelson's important work on exponential ARCH, EGARCH, conditional betas, and rolling estimators is here. For financial engineers and others who wish to apply these models to the pricing of derivative securities, the papers in this volume forge important links between the continuous time theoretical models and the discrete time empirical models used to estimate the crucial volatility process." --WAYNE E. FERSON, University of Washington

"This book is an essential companion for any graduate student or researcher working in financial econometrics. It contains key papers for better understanding volatility modeling of financial time series, especially the link between discrete-time models of the ARCH family and continuous-time stochastic volatility models. The book's first two-thirds contains seminal papers of Dan Nelson, a major contributor to the analysis of the link between the two types of models. A Central issue is the filtering performance provided by ARCH models for the continuous-time unobserved stochastic volatility. The book's final part presents major papers on specification and estimation of continuous-time processes. All of these reference papers will be read time and time again to absorb their full substance. The introduction by Tim Bollersley and Peter Rossi offers a clear organizing canvas that puts all of the papers in the proper perspective." --Rene Garcia, Universite de Montreal in JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (June 2000)