바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.22 No.2

Citation Share

A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.2, pp.159-168
https://doi.org/10.7468/jksmeb.2015.22.2.159
JEONG, DARAE
KIM, YOUNG ROCK
LEE, SEUNGGYU
CHOI, YONGHO
LEE, WOONG-KI
SHIN, JAE-MAN
AN, HYO-RIM
HWANG, HYEONGSEOK
KIM, HJUNSEOK
JEONG,, D. , KIM,, Y. R. , LEE,, S. , CHOI,, Y. , LEE,, W. , SHIN,, J. , AN,, H. , HWANG,, H. , & KIM,, H. (2015). A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(2), 159-168, https://doi.org/10.7468/jksmeb.2015.22.2.159

Abstract

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.

keywords
jump-diffusion, Simpson's rule, non-uniform grid, implicit finite difference method, derivative securities.

Reference

1.

Carr, P.;Cousot, L.;. (2011). A PDE approach to jump-diffusions. Quant. Fin., 11(1), 33-52. 10.1080/14697688.2010.531042.

2.

Cheang, G.;Chiarella, C.;. (2011). A modern view on Merton's jump-diffusion model. Quant. Fin. Res. Cent., 287.

3.

Duffy, D.J.;. Finite Difference methods in financial engineering: a Partial Differential Equation approach.

4.

Feng, L.;Linetsky, V.;. (2008). Pricing options in jump-diffusion models: an extrapolation approach. Oper. Res., 56(2), 304-325. 10.1287/opre.1070.0419.

5.

Kremer, J.W.;Roenfeldt, R.L.;. (1993). Warrant pricing: jump-diffusion vs. Black-Scholes. J. Finan. Quant. Anal., 28(2), 255-272. 10.2307/2331289.

6.

Kwon, Y.H.;Lee, Y.;. (2011). A second-order finite difference method for option pricing under jump-diffusion models. SIAM J. Numer. Anal., 49(6), 2598-2617. 10.1137/090777529.

7.

Tankov, P.;. Financial modelling with jump processes.

8.

Lee, S.;Li, Y.;Choi, Y.;Hwang, H.;Kim, J.;. (2014). Accurate and efficient computations for the Greeks of European multi-asset options. J. KSIAM, 18(1), 61-74.

9.

Merton, R.C.;. (1976). Option pricing when underlying stock returns are discontinuous. J. Polit. Econ., 3(1), 125-144.

10.

Using MATLAB.

11.

Windcliff, H.;Forsyth, P.A.;Vetzal, K.R.;. (2004). Analysis of the stability of the linear boundary condition for the Black-Scholes equation. J. Comput. Fin., 8, 65-92.

12.

Black, F.;Scholes, M.;. (1973). The pricing of options and corporate liabilities. J. Polit. Econ., 81, 637-654. 10.1086/260062.

13.

Briani, M.;Natalini, R.;Russo, G.;. (2007). Implicit-explicit numerical schemes for jump-diffusion processes. Calcolo, 44(1), 33-57. 10.1007/s10092-007-0128-x.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy