Estimation of integrated volatility in continuous time financial models with applications to goodness-of-fit testing

Mathias Vetter, Mark Podolskij () and Holger Dette

No 2004,32, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + sigma (t,Xt) dWt 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 sigma 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 Xt 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.

Keywords: continuous time financial model; model diagnostics; diffusion process; heteroscedasticity; pseudo residuals; parametric bootstrap (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200432

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