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Coupling index and stocks

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  • Benjamin Jourdain
  • Mohamed Sbai

Abstract

In this paper, we are interested in continuous-time models in which the index level induces 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 from 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, 2012. "Coupling index and stocks," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 805-818, March.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:5:p:805-818
    DOI: 10.1080/14697681003785959
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    File URL: http://hdl.handle.net/10.1080/14697681003785959
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    Cited by:

    1. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01686114, HAL.

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