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A link between complete models with stochastic volatility and ARCH models

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  • Thierry Jeantheau

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    Abstract

    In this paper, we propose a heteroskedastic model in discrete time which converges, when the sampling interval goes to zero, towards the complete model with stochastic volatility in continuous time described in Hobson and Rogers (1998). Then, we study its stationarity and moment properties. In particular, we exhibit a specific model which shares many properties with the GARCH(1,1) model, establishing a clear link between the two approaches. We also prove the consistency of the pseudo conditional likelihood maximum estimates for this specific model. Copyright Springer-Verlag Berlin/Heidelberg 2004

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    File URL: http://hdl.handle.net/10.1007/s00780-003-0103-6
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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 8 (2004)
    Issue (Month): 1 (January)
    Pages: 111-131

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    Handle: RePEc:spr:finsto:v:8:y:2004:i:1:p:111-131

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    Related research

    Keywords: ARCH models; stochastic volatility; diffusion approximation; Markov chain; asymptotic theory;

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