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Sample and Implied Volatility in GARCH Models

Lajos Horvath, Piotr Kokoszka and Ricardas Zitikis

Journal of Financial Econometrics, 2006, vol. 4, issue 4, 617-635

Abstract: The unconditional variance of various GARCH-type models is a function h(theta) of the parameter vector theta which is estimated by theta. For most models used in practice, closed-form expressions of h(.) have been found. On the contrary, the unconditional variance can be estimated by the sample variance sigma^2. This article establishes the asymptotic distributions of the differences sigma^2 - h(theta) and &sigma^2 - h(theta) for broad classes of GARCH-type models. Even though both limit distributions are normal, the asymptotic variances are not equal. Potential practical consequences of these results are discussed. Copyright 2006, Oxford University Press.

Date: 2006
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Handle: RePEc:oup:jfinec:v:4:y:2006:i:4:p:617-635