HAL : hal-00350652, version 2

arXiv : 0911.2834

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Coupling Index and Stocks

Benjamin Jourdain 1, Mohamed Sbai 1

(17/12/2008)

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.

1 :	Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique (CERMICS)
	INRIA – Ecole des Ponts ParisTech

Domaine

:

Économie et finance quantitative/Pricing

Mots Clés : Index modeling – calibration – non-parametric estimation

hal-00350652, version 2

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Contributeur : Mohamed Sbai <>

Soumis le : Samedi 14 Novembre 2009, 22:31:53

Dernière modification le : Dimanche 15 Novembre 2009, 07:29:38