Summary
This paper presents the implementation to the class of jump diffusion models of the approach used by Boyarchenko and Levendorskii (2002) in the case of exponential Lévy models. We show that this approach is more computationally efficient than the semi-closed form solutions formerly obtained by Kou (2002). A brand new model is then presented. It extends and generalizes Kou model.
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How to Price Efficiently European Options in Some Geometric Lévy Processes Models?
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I. INTRODUCTIONIt is now well recognized that the Gaussian hypothesis for financial assets returns is a convenient assumption but which is clearly rejected when returns are computed with high or medium frequencies. To depart from the traditional hypothesis a general modelling has been put forward for the recent years. It can be expressed in the following way: asset prices are exponentials of Lévy processes, otherwise stated the returns are Lévy processes or asset prices are geometric Lévy processes. The class of Lévy processes is very large and includes arithmetic Brownian motion. Amongst the many candidates to describe financial series and frequently used are: Generalized Hyperbolic, Normal Inverse Gaussian, Meixner, Variance Gamma, CGMY processes and of course jump diffusio...See the full content of this document
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