Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

Abstract

Autoregressive Conditional Heteroscedasticity (ARCH) models have successfully been employed in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of univariate and multivariate ARCH models, their estimating methods and the characteristics of financial time series, which are captured by volatility models, are presented. The number of possible conditional volatility formulations is vast. Therefore, a systematic presentation of the models that have been considered in the ARCH literature can be useful in guiding one’s choice of a model for exploiting future volatility, with applications in financial markets.

Key Words:

• ARCH models
• forecast volatility

Additional information

Notes on contributors

Stavros Degiannakis

Stavros Degiannakis Ph.D. student at the Department of Statistics, Athens University of Economics and Business. He has a first degree in Statistics from the Athens University of Economics and Business and an M.Sc. in Econometrics from the University of Essex, United Kingdom.

Evdokia Xekalaki

Evdokia Xekalaki Professor of Statistics at the Department of Statistics, Athens University of Economics and Business. Her research interests include Distribution Theory, Stochastic Model Building and Evaluation, ARCH models, Inventory Decision Problems, Accident Theory, Survey Sampling, Statistical Indices, Statistical Demography, Statistical Methodology in Actuarial Practice. She is an elected member of the International Statistical Institute, a Fellow of the Royal Statistical Society, a member of the American Statistical Association, and a member of several other societies. Professor Xekalaki is the Editor-in-Chief of Quality Technology and Quantitative Management for the European region, and a member of the Editorial Board of the Journal of Applied Stochastic Models in Business and Industry. She has published more than 50 papers in international scientific journals.