### 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 |
---|---|

Journal | Economic Computation and Economic Cybernetics Studies and Research |

Volume | 48 |

Issue number | 1 |

Publication status | Published - 2014 Jan 1 |

### Fingerprint

### ASJC Scopus subject areas

- Economics and Econometrics
- Computer Science Applications
- Applied Mathematics

### Cite this

*Economic Computation and Economic Cybernetics Studies and Research*,

*48*(1).

**A series solution of Black-Scholes equation under jump diffusion model.** / Moon, Kyoung Sook; Kim, Hongjoong; Jeong, Yunju.

Research output: Contribution to journal › Article

*Economic Computation and Economic Cybernetics Studies and Research*, vol. 48, no. 1.

}

TY - JOUR

T1 - A series solution of Black-Scholes equation under jump diffusion model

AU - Moon, Kyoung Sook

AU - Kim, Hongjoong

AU - Jeong, Yunju

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Black-Scholes equation

KW - Jump-diffusion

KW - Option pricing

KW - Partial integro-differential equation

KW - Polynomial chaos

UR - http://www.scopus.com/inward/record.url?scp=84902192813&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902192813&partnerID=8YFLogxK

M3 - Article

VL - 48

JO - The BMJ

JF - The BMJ

SN - 0730-6512

IS - 1

ER -