### Abstract

We introduce a series solution for a partial integro-differential equation which arises in option pricing when the Black-Scholes partial differential equations are considered under jump diffusion models. We construct a polynomial chaos solution using the Taylor expansion with respect to Hermite polynomials, which simplifies the integral term and derives a system of deterministic ordinary differential equations. Numerical examples show that the proposed method efficiently gives the desired accuracy for pricing options.

Original language | English |
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Journal | Economic Computation and Economic Cybernetics Studies and Research |

Volume | 48 |

Issue number | 1 |

Publication status | Published - 2014 |

### Keywords

- Black-Scholes equation
- Jump-diffusion
- Option pricing
- Partial integro-differential equation
- Polynomial chaos

### ASJC Scopus subject areas

- Economics and Econometrics
- Computer Science Applications
- Applied Mathematics

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## Cite this

Moon, K. S., Kim, H., & Jeong, Y. (2014). A series solution of Black-Scholes equation under jump diffusion model.

*Economic Computation and Economic Cybernetics Studies and Research*,*48*(1).