A SERIES SOLUTION OF BLACK-SCHOLES EQUATION UNDER JUMP DIFFUSION MODEL
- Authors
- Moon, Kyoung-Sook; Kim, Hongjoong; Jeong, Yunju
- Issue Date
- 2014
- Publisher
- ACAD ECONOMIC STUDIES
- Keywords
- Black-Scholes equation; jump-diffusion; polynomial chaos; partial integro-differential equation; option pricing
- Citation
- ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, v.48, no.1, pp.127 - 139
- Indexed
- SCIE
SSCI
SCOPUS
- Journal Title
- ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH
- Volume
- 48
- Number
- 1
- Start Page
- 127
- End Page
- 139
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/100988
- ISSN
- 0424-267X
- 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.
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