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A link between complete models with stochastic volatility and ARCH models

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  • Thierry Jeantheau

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

Suggested Citation

  • Thierry Jeantheau, 2004. "A link between complete models with stochastic volatility and ARCH models," Finance and Stochastics, Springer, vol. 8(1), pages 111-131, January.
    • Handle: RePEc:spr:finsto:v:8:y:2004:i:1:p:111-131
    DOI: 10.1007/s00780-003-0103-6
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    Cited by:

    1. Hafner, Christian M. & Laurent, Sebastien & Violante, Francesco, 2017. "Weak Diffusion Limits Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(3), pages 691-716, June.
    2. Buccheri, Giuseppe & Corsi, Fulvio & Flandoli, Franco & Livieri, Giulia, 2021. "The continuous-time limit of score-driven volatility models," Journal of Econometrics, Elsevier, vol. 221(2), pages 655-675.
    3. Taewook Kim & Ha Young Kim, 2019. "Forecasting stock prices with a feature fusion LSTM-CNN model using different representations of the same data," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-23, February.
    4. René Carmona, 2022. "The influence of economic research on financial mathematics: Evidence from the last 25 years," Finance and Stochastics, Springer, vol. 26(1), pages 85-101, January.
    5. Trifi Amine, 2006. "Issues of Aggregation Over Time of Conditional Heteroscedastic Volatility Models: What Kind of Diffusion Do We Recover?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-26, December.

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