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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.22 No.2

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

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

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Korea University)
KIM, YOUNG ROCK (Major in Mathematics Education, Hankuk University of Foreign Studies)
LEE, SEUNGGYU (Department of Mathematics, Korea University)
CHOI, YONGHO (Department of Mathematics, Korea University)
LEE, WOONG-KI (Business School, Korea University)
SHIN, JAE-MAN (Department of Financial Engineering, Korea University)
AN, HYO-RIM (Department of Financial Engineering, Korea University)
HWANG, HYEONGSEOK (Department of Financial Engineering, Korea University)
KIM, HJUNSEOK (Department of Mathematics, Korea University)
JEONG, DARAE, KIM, YOUNG ROCK, LEE, SEUNGGYU, CHOI, YONGHO, LEE, WOONG-KI, SHIN, JAE-MAN, AN, HYO-RIM, HWANG, HYEONGSEOK, & KIM, HJUNSEOK. (2015). A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL. 한국수학교육학회지시리즈B:순수및응용수학, 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.

참고문헌

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.

한국수학교육학회지시리즈B:순수및응용수학

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