Option pricing with discrete time jump processes

Dominique Guegan (dominique.guegan@univ-paris1.fr), Florian Ielpo and Hanjarivo Lalaharison
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Dominique Guegan: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Option pricing; Lévy processess; incomplete market; exponential affine stochastic discount factor; Minimal Entropy Martingale Measure; CAC 40; Pricing d'options; processus de Lévy; marchés incomplets (search for similar items in EconPapers)
Date: 2012-04
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00611706v2
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Published in 2012

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Related works:
Journal Article: Option pricing with discrete time jump processes (2013)
Working Paper: Option pricing with discrete time jump processes (2013)
Working Paper: Option pricing with discrete time jump processes (2012)
Working Paper: Option pricing with discrete time jump processes (2011)
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