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A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL
- Authors
- Jeong, Darae; Kim, Young Rock; Lee, Seunggyu; Choi, Yongho; Lee, Woong-Ki; Shin, Lae-Man; An, Hyo-Rim; Hwang, Hyeongseok; Kim, Junseok
- Issue Date
- 5월-2015
- Publisher
- KOREAN SOC MATHEMATICAL EDUCATION
- Keywords
- jump-diffusion; Simpson' s rule; non-uniform grid; implicit finite difference method; derivative securities
- Citation
- JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, v.22, no.2, pp.159 - 168
- Indexed
- KCI
- Journal Title
- JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS
- Volume
- 22
- Number
- 2
- Start Page
- 159
- End Page
- 168
- ISSN
- 1226-0657
- Abstract
- We propose a fast and robust finite difference method for Merton`s jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.
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