Encyclopedia of Financial Models II

ARCH/GARCH Models in Applied Financial Econometrics

ROBERT F. ENGLE, PhD

Michael Armellino Professorship in the Management of Financial Services and Director of the Volatility Institute, Leonard N. Stern School of Business, New York University

SERGIO M. FOCARDI, PhD

Partner, The Intertek Group

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Volatility is a key parameter used in many financial applications, from derivatives valuation to asset management and risk management. Volatility measures the size of the errors made in modeling returns and other financial variables. It was discovered that, for vast classes of models, the average size of volatility is not constant but changes with time and is predictable. Autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH) models, and stochastic volatility models are the main tools used to model and forecast volatility. Moving from single assets to portfolios made of multiple assets, not only are there idiosyncratic volatilities but also correlations and covariances between assets that are time varying and predictable. Multivariate ARCH/GARCH models and dynamic factor models, eventually in a Bayesian framework, are the basic tools used to forecast correlations and covariances.

In this entry we discuss the modeling of the time behavior of the uncertainty related to many econometric models when applied to financial data. Finance practitioners ...