A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL
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초록
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 effiency. 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.
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 effiency. 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.
참고문헌 (13)
- F. Black, "The pricing of options and corporate liabilities", J. Polit. Econ, 81, pp.637~654 (1973)
- M. Briani, "Implicit-explicit numerical schemes for jump-diffusion processes", Calcolo, 44(1), pp.33~57 (2007)
- P. Carr, "A PDE approach to jump-diffusions", Quant. Fin, 11(1), pp.33~52 (2011)
- G. Cheang, "A modern view on Merton's jump-diffusion model", Quant. Fin. Res. Cent, 287 (2011)
- D.J. Duffy, "Finite Difference methods in financial engineering: a Partial Differential Equation approach" (2006), John Wiley & Sons
- L. Feng, "Pricing options in jump-diffusion models: an extrapolation approach", Oper. Res, 56(2), pp.304~325 (2008)
- J.W. Kremer, "Warrant pricing: jump-diffusion vs. Black-Scholes", J. Finan. Quant. Anal, 28(2), pp.255~272 (1993)
- Y.H. Kwon, "A second-order finite difference method for option pricing under jump-diffusion models", SIAM J. Numer. Anal, 49(6), pp.2598~2617 (2011)
- 김준석, "ACCURATE AND EFFICIENT COMPUTATIONS FOR THE GREEKS OF EUROPEAN MULTI-ASSET OPTIONS", Journal of the Korean Society for Industrial and Applied Mathematics, 18(1), pp.61~74 (2014), 한국산업응용수학회[DOI]
- R.C. Merton, "Option pricing when underlying stock returns are discontinuous", J. Polit. Econ, 3(1), pp.125~144 (1976)
- P. Tankov, "Financial modelling with jump processes" (2003), CRC press
- "Using MATLAB" (1998)[URL]
- H. Windcliff, "Analysis of the stability of the linear bound-ary condition for the Black-Scholes equation", J. Comput. Fin, 8, pp.65~92 (2004)