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Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models

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Abstract

In mathematical finance a popular approach for pricing options under some Lévy model would be to consider underlying that follows a Poisson jump diffusion process. As it is well known this results in a partial integro-differential equation (PIDE) that usually does not allow an analytical solution, while a numerical solution also faces some problems. In this paper we develop a new approach on how to transform the PIDE into a class of so-called pseudo-parabolic equations which are well known in mathematical physics but are relatively new for mathematical finance. As an example we will discuss several jump-diffusion models which Lévy measure allows such a transformation.

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Authors and Affiliations

  1. New York University Polytechnic Institute, 6 Metro Tech Center, RH 517E, Brooklyn, NY, 11201, USA

    Andrey Itkin

  2. Morgan Stanley, 585 Broadway, New York, NY, 10036, USA

    Peter Carr

  3. New York University, New York, NY, USA

    Peter Carr

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  1. Andrey Itkin
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  2. Peter Carr
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Correspondence to Andrey Itkin.

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Itkin, A., Carr, P. Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models. Comput Econ 40, 63–104 (2012). https://doi.org/10.1007/s10614-011-9269-8

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  • DOI: https://doi.org/10.1007/s10614-011-9269-8

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