New Frontiers for Arch Models

29 Pages Posted: 3 Nov 2008

See all articles by Robert F. Engle

Robert F. Engle

New York University - Leonard N. Stern School of Business - Department of Economics; New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)

Date Written: June 2002

Abstract

In the 20 years following the publication of the ARCH model, there has been a vast quantity of research uncovering the properties of competing volatility models.Wide-ranging applications to financial data have discovered important stylized facts and illustrated both the strengths and weaknesses of the models. There are now many surveys of this literature.This paper looks forward to identify promising areas of new research. The paper lists five new frontiers. It briefly discusses three high frequency volatility models, large-scale multivariate ARCH models, and derivatives pricing models. Two further frontiers are examined in more detail application of ARCH models to the broadclass of non-negative processes, and use of Least Squares Monte Carlo to examine non-linear properties of any model that can be simulated. Using this methodology, the paper analyzes more general types of ARCH models, stochastic volatility models, long memory models and breaking volatility models. The volatility of volatility is defined,estimated and compared with option implied volatilities.

Keywords: ARCH, GARCH, volatility, non-linear process, non-negative process, option pricing, stochastic volatility, long memory, Least Squares Monte Carlo, ACD, Multiplicative Error Model, MEM

Suggested Citation

Engle, Robert F., New Frontiers for Arch Models (June 2002). NYU Working Paper No. FIN-02-037. Available at SSRN: https://ssrn.com/abstract=1294215

Robert F. Engle (Contact Author)

New York University - Leonard N. Stern School of Business - Department of Economics ( email )

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New York University (NYU) - Department of Finance

Stern School of Business
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National Bureau of Economic Research (NBER)

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