Option Pricing with Discrete Time Jump Processes
Université Paris I Panthéon-Sorbonne - CERMSEM; Lombard Odier Darier Hentsch & Cie
Universite Paris 1 Pantheon-Sorbonne
Université Paris I Panthéon-Sorbonne - CERMSEM
June 30, 2011
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.
Number of Pages in PDF File: 29working papers series
Date posted: July 1, 2011
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo1 in 0.422 seconds