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Option pricing with discrete time jump processes

Author

Listed:
  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Florian Ielpo

    (Lombard Odier Asset Management - Lombard Odier Asset Management)

  • Hanjarivo Lalaharison

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we propose new option pricing models based on class of models with jumps contained in the Lévy-type based models (NIG-Lévy, Schoutens, 2003, Merton-jump, Merton, 1976 and Duan based model, Duan et al., 2007). By combining these different classes of models with several volatility dynamics of the GARCH type, we aim at taking into account the dynamics of financial returns in a realistic way. The associated risk neutral dynamics of the time series models is obtained through two different specifications for the pricing kernel: we provide a characterization of the change in the probability measure using the Esscher transform and the Minimal Entropy Martingale Measure. We finally assess empirically the performance of this modelling approach, using a dataset of European options based on the S&P 500 and on the CAC 40 indices. Our results show that models involving jumps and a time varying volatility provide realistic pricing and hedging results for options with different kinds of time to maturities and moneyness. These results are supportive of the idea that a realistic time series model can provide realistic option prices making the approach developed here interesting to price options when option markets are illiquid or when such markets simply do not exist.

Suggested Citation

  • Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2013. "Option pricing with discrete time jump processes," Post-Print hal-00964950, HAL.
    • Handle: RePEc:hal:journl:hal-00964950
    DOI: 10.1016/j.jedc.2013.07.003
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    Citations

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    Cited by:

    1. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2020. "The contribution of intraday jumps to forecasting the density of returns," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02505861, HAL.
    2. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2020. "The contribution of intraday jumps to forecasting the density of returns," Post-Print halshs-02505861, HAL.
    3. Chorro, Christophe & Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2018. "Testing for leverage effects in the returns of US equities," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 290-306.
    4. Chorro, Christophe & Ielpo, Florian & Sévi, Benoît, 2020. "The contribution of intraday jumps to forecasting the density of returns," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    5. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," Documents de travail du Centre d'Economie de la Sorbonne 14022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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