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Option pricing with discrete time jump processes

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Abstract

In this paper we propose new option pricing models based on class of models with jump contain in the Lévy-type based models (NIG-Lévy, Merton-jump (Merton 1976) and Duan based model (Duan 2007)). By combining these different class 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 results for options with different kinds of time to maturities and moneyness. Furthermore, our results provide evidence of consistency between historical and risk neutral distributions, making the approach developed here interesting to price option when option markets are illiquid or when such markets simply do not exist

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  • Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2011. "Option pricing with discrete time jump processes," Documents de travail du Centre d'Economie de la Sorbonne 11037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:11037
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    Cited by:

    1. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effects in the Returns of US Equities," Documents de travail du Centre d'Economie de la Sorbonne 14022r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2017.
    2. repec:hal:journl:halshs-00973922 is not listed on IDEAS
    3. 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.

    More about this item

    Keywords

    Option pricing; Lévy processes; exponential affine stochastic discount factor; minimal entropy martingale measure; CAC 40; S&P 500;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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