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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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    Bibliographic 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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    Web page: http://www.bankofgreece.gr
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    Related research

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

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    1. Dimitrios Sideris, 2004. "Testing for Long-Run PPP in a System Context: Evidence for the US, Germany and Japan," Working Papers 19, Bank of Greece.
    2. Dimitrios Sideris & Nicholas G. Zonzilos, 2005. "The Greek Model of the European System of Central Banks Multi-Country Model," Working Papers 20, Bank of Greece.
    3. Dellas, Harris & Tavlas, George, 2003. "Wage Rigidity and Monetary Union," CEPR Discussion Papers 3679, C.E.P.R. Discussion Papers.
    4. Theodoros S. Papaspyrou, 2004. "EMU Strategies: Lessons from Past Experience in View of EU Enlargement," Working Papers 11, Bank of Greece.
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    7. George Hondroyiannis & P.A.V.B. Swamy & George S. Tavlas & Michael Ulan, 2005. "Some Further Evidence on Exchange-Rate Volatility and Exports," Working Papers 28, Bank of Greece.
    8. George Hondroyiannis & Sophia Lazaretou, 2007. "Inflation persistence during periods of structural change: an assessment using Greek data," Empirica, Springer, vol. 34(5), pages 453-475, December.
    9. Panayotis Kapopoulos & Sophia Lazaretou, 2005. "Does Corporate Ownership Structure Matter for Economic Growth? A Cross-Country Analysis," Working Papers 21, Bank of Greece.
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    19. Heather D Gibson & Euclid Tsakalotos, 2003. "Capital Flows and Speculative Attacks in Prospective EU Member States," Working Papers 06, Bank of Greece.
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    21. Nicholas G. Zonzilos, 2004. "Econometric Modelling at the Bank of Greece," Working Papers 14, Bank of Greece.
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    23. George Stubos & Ioannis Tsikripis, 2005. "Regional Integration Challenges in South East Europe: Banking Sector Trends," Working Papers 24, Bank of Greece.
    24. Alexandros E. Milionis, 2003. "Modelling Economic Time Series in the Presence of Variance Non-Stationarity: A Practical Approach," Working Papers 07, Bank of Greece.
    25. Stephen G. Hall & Nicholas G. Zonzilos, 2003. "An Indicator Measuring Underlying Economic Activity in Greece," Working Papers 04, Bank of Greece.
    26. Yiannis Stournaras, 2005. "Aggregate Supply and Demand, the Real Exchange Rate and Oil Price Denomination," Working Papers 26, Bank of Greece.
    27. Eleni Angelopoulou, 2005. "The Comparative Performance of Q-type and Dynamic Models of Firm Investment: Empirical Evidence from the UK," Working Papers 27, Bank of Greece.
    28. Thanasis N. Christodoulopoulos & Ioulia Grigoratou, 2003. "The Effect of Dynamic Hedging of Options Positions on Intermediate-Maturity Interest Rates," Working Papers 08, Bank of Greece.
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    Cited by:
    1. John Williamson, 2006. "A worldwide system of reference rates," International Economics and Economic Policy, Springer, vol. 3(3), pages 341-352, December.
    2. Hans Genberg, 2006. "Exchange-Rate Arrangements an Financial Integration in East Asia: On a Collision Course?," Working Papers 122, Oesterreichische Nationalbank (Austrian Central Bank).
    3. 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.
    4. Otmar Issing, 2006. "Europe's Hard Fix: The Euro Area," Working Papers 39, Bank of Greece.

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