Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/22544
Authors: 
Vetter, Mathias
Podolskij, Mark
Dette, Holger
Year of Publication: 
2004
Series/Report no.: 
Technical Report / Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2004,32
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.
Subjects: 
continuous time financial model
model diagnostics
diffusion process
heteroscedasticity
pseudo residuals
parametric bootstrap
Document Type: 
Working Paper

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