### 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.

Original language | English (US) |
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Pages (from-to) | 63-104 |

Number of pages | 42 |

Journal | Computational Economics |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jun 2012 |

### Keywords

- Finite-difference scheme
- General stable tempered process
- Jump-diffusion
- Numerical method
- Pseudo-parabolic equations
- The Green function

### ASJC Scopus subject areas

- Economics, Econometrics and Finance (miscellaneous)
- Computer Science Applications

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## Cite this

*Computational Economics*,

*40*(1), 63-104. https://doi.org/10.1007/s10614-011-9269-8