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Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing

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Author Info
HOLGER DETTE
MARK PODOLSKIJ
MATHIAS VETTER

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Abstract

Properties of a specification test for the parametric form of the variance function in diffusion processes are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the variable "x" it is known that the corresponding statistics have an asymptotic normal distribution. However, most models of mathematical finance use a volatility function which depends on the state "x". In this paper we prove that in the general case, where "σ" depends also on "x" the estimates of integrals of the volatility converge stably in law to random variables with a non-standard limit distribution. The limit distribution depends on the diffusion process "X""t" itself and we use this result to develop a bootstrap test for the parametric form of the volatility function, which is consistent in the general diffusion model. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9469.2006.00479.x
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Article provided by Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association and Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

Volume (Year): 33 (2006)
Issue (Month): 2 ()
Pages: 259-278
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Handle: RePEc:bla:scjsta:v:33:y:2006:i:2:p:259-278

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  1. Mark Podolskij & Mathias Vetter, 2009. "Understanding limit theorems for semimartingales: a short survey," CREATES Research Papers 2009-47, School of Economics and Management, University of Aarhus. [Downloadable!]
  2. Silja Kinnebrock & Mark Podolskij, 2007. "A Note on the Central Limit Theorem for Bipower Variation of General Functions," OFRC Working Papers Series 2007fe03, Oxford Financial Research Centre. [Downloadable!]
  3. Mark Podolskij & Daniel Ziggel, 2007. "A Range-Based Test for the Parametric Form of the Volatility in Diffusion Models," CREATES Research Papers 2007-26, School of Economics and Management, University of Aarhus. [Downloadable!]
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