Exact Elliptical Distributions for Models of Conditionally Random Financial Volatility

George A. Christodoulakis () and Stephen Satchell
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Stephen Satchell: Trinity College, University of Cambridge and Bank of Greece

No 32, Working Papers from 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.

Keywords: Elliptical Distributions; Financial Asset Returns; Conditional Volatility; GARCH (search for similar items in EconPapers)
JEL-codes: C22 G11 G12 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2006-01
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