Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 60. ARCH/GARCH Models in Applied Financial Econometrics

ROBERT F. ENGLE, PhD

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

SERGIO M. FOCARDI

Partner, The Intertek Group

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

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, we find that not only idiosyncratic volatilities but also correlations and covariances between assets 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.

Keywords: autoregressive conditional duration, ACD-GARCH, autoregressive conditional heteroskedasticity (ARCH), autoregressive models, conditional autoregressive value at risk (CAViaR), dynamic ...