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A link between complete models with stochastic volatility and ARCH models

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.
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Submitted on : Wednesday, May 2, 2012 - 4:43:02 PM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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Thiery Jeantheau. A link between complete models with stochastic volatility and ARCH models. Finance and Stochastics, Springer Verlag (Germany), 2004, 8 (1), pp.111--131. ⟨10.1007/s00780-003-0103-6⟩. ⟨hal-00693440⟩

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