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New frontiers for arch models

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Author Info
Robert Engle (Department of Finance, Stern School of Business, New York University, New York, NY 10012, USA)

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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 broad class 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 analyses 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. Copyright © 2002 John Wiley & Sons, Ltd.

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File URL: http://hdl.handle.net/10.1002/jae.683
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File URL: http://qed.econ.queensu.ca:80/jae/2002-v17.5/
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Publisher Info
Article provided by John Wiley & Sons, Ltd. in its journal Journal of Applied Econometrics.

Volume (Year): 17 (2002)
Issue (Month): 5 ()
Pages: 425-446
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Handle: RePEc:jae:japmet:v:17:y:2002:i:5:p:425-446

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June. [Downloadable!] (restricted)
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  2. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-78, December. [Downloadable!] (restricted)
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  3. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December. [Downloadable!] (restricted)
  4. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February. [Downloadable!] (restricted)
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  5. McCurdy, Thomas H. & Stengos, Thanasis, 1992. "A comparison of risk-premium forecasts implied by parametric versus nonparametric conditional mean estimators," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 225-244. [Downloadable!] (restricted)
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  6. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59. [Downloadable!] (restricted)
  7. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA. [Downloadable!]
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  8. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  9. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-35, April.
  10. Robert F. Engle & Kevin Sheppard, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series 2001-15, Department of Economics, UC San Diego. [Downloadable!]
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  11. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc. [Downloadable!] (restricted)
  12. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September. [Downloadable!] (restricted)
  13. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January. [Downloadable!] (restricted)
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  14. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  15. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Blackwell Publishing, vol. 16(3), pages 245-69, July. [Downloadable!] (restricted)
  16. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  17. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348. [Downloadable!] (restricted)
  18. Robert F. Engle & Joshua Rosenberg, 1998. "Testing the Volatility Term Structure using Option Hedging Criteria," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-031, New York University, Leonard N. Stern School of Business-. [Downloadable!]
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  19. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  20. Jaesun Noh & Robert F. Engle & Alex Kane, 1994. "Forecasting Volatility and Option Prices of the S&P 500 Index," University of California at San Diego, Economics Working Paper Series 93-32r, Department of Economics, UC San Diego. [Downloadable!]
  21. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
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  22. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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