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Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility

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Author Info
George A. Christodoulakis () (Bank of Greece and Manchester Business School)
Stephen E Satchell (Trinity College, University of Cambridge and Bank of Greece)

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Abstract

Assuming the time series of random returns to be jointly elliptical, we derive a relationship between its conditional variance and the probability density function of the conditioning set. In the case that such a relationship is linear in a quadratic form for of the conditioning variables, we show that the probability density function of the conditioning variables is multivariate t. This result is then applied to models of conditionally random volatility and used to derive exact results for the GARCH(p,q) class of processes previously thought to be intractable.

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File URL: http://www.bankofgreece.gr/BogEkdoseis/Paper200632.pdf
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Publisher Info
Paper provided by Bank of Greece in its series Working Papers with number 32.

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Length: 21 pages
Date of creation: Jan 2006
Date of revision:
Handle: RePEc:bog:wpaper:32

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Related research
Keywords: Elliptical Distributions; Financial Asset Returns; Conditional Volatility; GARCH;

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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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. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127. [Downloadable!] (restricted)
  2. Keith Vorkink & Douglas J. Hodgson & Oliver Linton, 2002. "Testing the capital asset pricing model efficiently under elliptical symmetry: a semiparametric approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 617-639. [Downloadable!]
    Other versions:
  3. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July. [Downloadable!] (restricted)
    Other versions:
  4. Easley, David & O'Hara, Maureen, 1992. " Time and the Process of Security Price Adjustment," Journal of Finance, American Finance Association, vol. 47(2), pages 576-605, June.
  5. 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)
  6. Keith Vorkink, 2003. "Return Distributions and Improved Tests of Asset Pricing Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(3), pages 845-874, July. [Downloadable!] (restricted)
  7. Foster, F Douglas & Viswanathan, S, 1993. "The Effect of Public Information and Competition on Trading Volume and Price Volatility," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(1), pages 23-56. [Downloadable!] (restricted)
  8. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November. [Downloadable!] (restricted)
  9. Owen, Joel & Rabinovitch, Ramon, 1983. " On the Class of Elliptical Distributions and Their Applications to the Theory of Portfolio Choice," Journal of Finance, American Finance Association, vol. 38(3), pages 745-52, June. [Downloadable!] (restricted)
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Cited by:
(explanations, 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. Sven W. Arndt, 2006. "Regional Currency Arrangements in North America," Working Papers 40, Bank of Greece. [Downloadable!]
    Other versions:
  2. George S. Tavlas & P.A.V.B. Swamy, 2006. "The New Keynesian Phillips Curve and Inflation Expectations: Re-Specification and Interpretation," Working Papers 34, Bank of Greece. [Downloadable!]
    Other versions:
  3. Hans Genberg, 2006. "Exchange-Rate Arrangements and Financial Integration in East Asia: On a Collision Course?," Working Papers 41, Bank of Greece. [Downloadable!]
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  4. Richard N. Cooper & Michael Bordo & Harold James, 2006. "What About a World Currency? Proposal for a Common Currency among Rich Democracies. One World Money, Then and Now," Working Papers 44, Bank of Greece. [Downloadable!]
  5. Andreas S. Andreou & George A. Zombanakis, 2006. "Computational Intelligence in Exchange-Rate Forecasting," Working Papers 49, Bank of Greece. [Downloadable!]
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