Option Pricing with Discrete Time Jump Processes

29 Pages Posted: 1 Jul 2011

See all articles by Florian Ielpo

Florian Ielpo

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES); Unigestion

Dominique Guegan

Université Paris I Panthéon-Sorbonne

Hanjarivo Lalaharison

Université Paris I Panthéon-Sorbonne - CERMSEM

Date Written: June 30, 2011

Abstract

In this paper we propose new option pricing models based on two classes of discrete Lévy-type processes. By combining these Lévy processes with several volatility dynamics of the GARCH type, we aim to take 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 CAC 40. Our empirical findings show that discrete time Lévy based models behave well regardless of the volatility dynamics and of the pricing kernel. A different specification is however required to obtain the best results for options with a shorter or longer maturity.

Suggested Citation

Ielpo, Florian and Guegan, Dominique and Lalaharison, Hanjarivo, Option Pricing with Discrete Time Jump Processes (June 30, 2011). Available at SSRN: https://ssrn.com/abstract=1875492 or http://dx.doi.org/10.2139/ssrn.1875492

Florian Ielpo (Contact Author)

Université Paris I Panthéon-Sorbonne - Centre d'Economie de la Sorbonne (CES) ( email )

106-112 Boulevard de l'hopital
106-112 Boulevard de l'Hôpital
Paris Cedex 13, 75647
France

Unigestion ( email )

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CP 387
Genève 12, CH 1211
Switzerland

Dominique Guegan

Université Paris I Panthéon-Sorbonne ( email )

106 avenue de lhopital
75634 Paris Cedex 13
Paris, IL
France

Hanjarivo Lalaharison

Université Paris I Panthéon-Sorbonne - CERMSEM ( email )

106-112, Boulevard de l'Hôpital
Paris, 75647
France

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