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Coupling Index and Stocks

Author

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  • Benjamin Jourdain

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech)

  • Mohamed Sbai

    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique - Inria - Institut National de Recherche en Informatique et en Automatique - ENPC - École des Ponts ParisTech)

Abstract

In this paper, we are interested in continuous time models in which the index level induces some feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the log-returns of each stock may be decomposed into a systemic part proportional to the log-returns of the index plus an idiosyncratic part. We show that, when the number of stocks in the index is large, this model may be approximated by a local volatility model for the index and a stochastic volatility model for each stock with volatility driven by the index. This result is useful in a calibration perspective : it suggests that one should first calibrate the local volatility of the index and then calibrate the dynamics of each stock. We explain how to do so in the limiting simplified model and in the original model.

Suggested Citation

  • Benjamin Jourdain & Mohamed Sbai, 2008. "Coupling Index and Stocks," Working Papers hal-00350652, HAL.
    • Handle: RePEc:hal:wpaper:hal-00350652
    Note: View the original document on HAL open archive server: https://hal.science/hal-00350652v2
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    Keywords

    Index modeling; calibration; non-parametric estimation;
    All these keywords.

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