### 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) |
---|---|

Pages (from-to) | 63-104 |

Number of pages | 42 |

Journal | Computational Economics |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jun 2012 |

### Fingerprint

### 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

### Cite this

*Computational Economics*,

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

**Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models.** / Itkin, Andrey; Carr, Peter.

Research output: Contribution to journal › Article

*Computational Economics*, vol. 40, no. 1, pp. 63-104. https://doi.org/10.1007/s10614-011-9269-8

}

TY - JOUR

T1 - Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models

AU - Itkin, Andrey

AU - Carr, Peter

PY - 2012/6

Y1 - 2012/6

N2 - 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.

AB - 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.

KW - Finite-difference scheme

KW - General stable tempered process

KW - Jump-diffusion

KW - Numerical method

KW - Pseudo-parabolic equations

KW - The Green function

UR - http://www.scopus.com/inward/record.url?scp=84860919189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860919189&partnerID=8YFLogxK

U2 - 10.1007/s10614-011-9269-8

DO - 10.1007/s10614-011-9269-8

M3 - Article

VL - 40

SP - 63

EP - 104

JO - Computational Economics

JF - Computational Economics

SN - 0927-7099

IS - 1

ER -