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Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility

Author

Listed:
  • George A. Christodoulakis

    (Bank of Greece and Manchester Business School)

  • Stephen E Satchell

    (Trinity College, University of Cambridge and Bank of Greece)

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.

Suggested Citation

  • George A. Christodoulakis & Stephen E Satchell, 2006. "Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility," Working Papers 32, Bank of Greece.
    • Handle: RePEc:bog:wpaper:32
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    References listed on IDEAS

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    Cited by:

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    3. Otmar Issing, 2006. "Europe's Hard Fix: The Euro Area," Working Papers 39, Bank of Greece.
    4. P. Swamy & George Tavlas, 2007. "The New Keynesian Phillips Curve and Inflation Expectations: Re-Specification and Interpretation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(2), pages 293-306, May.

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    More about this item

    Keywords

    Elliptical Distributions; Financial Asset Returns; Conditional Volatility; GARCH;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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