What good is a volatility model

What good is a - Q U A N T I T A T I V E F I N A N C E V O L U M E 1(2001 237245 INSTITUTE O F PHYSICS PUBLISHING RE S E A R C H PA P E R

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QUANTITATIVE FINANCE VOLUME 1 (2001) 237–245 R ESEARCH P APER INSTITUTE OF PHYSICS PUBLISHING quant.iop.org What good is a volatility model? Robert F Engle and Andrew J Patton Department of Finance, NYU Stern School of Business and Department of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508, USA Received 15 October 2000 Abstract A volatility model must be able to forecast volatility; this is the central requirement in almost all ±nancial applications. In this paper we outline some stylized facts about volatility that should be incorporated in a model: pronounced persistence and mean-reversion, asymmetry such that the sign of an innovation also affects volatility and the possibility of exogenous or pre-determined variables in²uencing volatility. We use data on the Dow Jones Industrial Index to illustrate these stylized facts, and the ability of GARCH-type models to capture these features. We conclude with some challenges for future research in this area. 1. Introduction A volatility model should be able to forecast volatility. Virtually all the ±nancial uses of volatility models entail forecasting aspects of future returns. Typically a volatility model is used to forecast the absolute magnitude of returns, but it may also be used to predict quantiles or, in fact, the entire density. Suchforecastsareusedinriskmanagement, derivative pricing and hedging, market making, market timing, portfolio selection and many other ±nancial activities. In each, it is the predictability of volatility that is required. A risk manager must know today the likelihood that his portfolio will decline in the future. An option trader will want to know the volatility that can be expected over the future life of the contract. To hedge this contract he will also want to know how volatile is this forecast volatility. A portfolio manager may want to sell a stock or a portfolio before it becomes too volatile. A market maker may want to set the bid–ask spread wider when the future is believed to be more volatile. There is now an enormous body of research on volatility models. This has been surveyed in several articles and continues to be a fruitful line of research for both practitioners and academics. As new approaches are proposed and tested, it is helpful to formulate the properties that these models should satisfy. At the same time, it is useful to discuss properties that standard volatility models do not appear to satisfy. We will concern ourselves in this paper only with the volatility of univariate series. Many of the same issues will arise in multivariate models. We will focus on the volatility of asset returns and consequently will pay very little attention to expected returns. 1.1. Notation First we will establish notation. Let P t be the asset price at time t and r t = ln (P t ) ln (P t 1 ) be the continuously compounded return on the asset over the period t 1to t . We de±ne the conditional mean and conditional variance as: m t = E t 1 [ r t ] (1) h t = E t 1 [ (r t m t ) 2 ] (2) where E t
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This note was uploaded on 02/28/2010 for the course ECO 211 taught by Professor Gilo during the Spring '10 term at Young Harris.

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What good is a - Q U A N T I T A T I V E F I N A N C E V O L U M E 1(2001 237245 INSTITUTE O F PHYSICS PUBLISHING RE S E A R C H PA P E R

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