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http://dx.doi.org/10.7468/jksmeb.2021.28.4.329

EFFICIENT AND ACCURATE FINITE DIFFERENCE METHOD FOR THE FOUR UNDERLYING ASSET ELS  

Hwang, Hyeongseok (Department of Financial Engineering, Korea University)
Choi, Yongho (Department of Mathematics and Big Data, Daegu University)
Kwak, Soobin (Department of Mathematics, Korea University)
Hwang, Youngjin (Department of Mathematics, Korea University)
Kim, Sangkwon (Department of Mathematics, Korea University)
Kim, Junseok (Department of Mathematics, Korea University)
Publication Information
The Pure and Applied Mathematics / v.28, no.4, 2021 , pp. 329-341 More about this Journal
Abstract
In this study, we consider an efficient and accurate finite difference method for the four underlying asset equity-linked securities (ELS). The numerical method is based on the operator splitting method with non-uniform grids for the underlying assets. Even though the numerical scheme is implicit, we solve the system of discrete equations in explicit manner using the Thomas algorithm for the tri-diagonal matrix resulting from the system of discrete equations. Therefore, we can use a relatively large time step and the computation of the ELS option pricing is fast. We perform characteristic computational test. The numerical test confirm the usefulness of the proposed method for pricing the four underlying asset equity-linked securities.
Keywords
four underlying asset ELS; equity-linked securities; Black-Scholes equation; finite difference scheme;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 W. Chen & S. Wang: A 2nd-order ADI finite difference method for a 2D fractional BlackScholes equation governing European two asset option pricing. Math. Comput. Simul. 171 (2020), 279-293.   DOI
2 R. Cont & E. Voltchkova: A finite difference scheme for option pricing in jump diffusion and exponential Lvy models. SIAM J. Numer. Anal. 43 (2005), no. 4, 1596-1626.   DOI
3 P. Glasserman: Monte Carlo methods in financial engineering. Springer Science and Business Media 53, 2013.
4 H. Jang, S. Kim, J. Han, S. Lee, J. Ban, H. Han, C. Lee, D. Jeong & J. Kim: Fast Monte Carlo simulation for pricing equity-linked securities. Comput. Econ. 56 (2019), 865-882.   DOI
5 H. Jang et al.: Fast ANDROID implimentation of Monte Carlo simulation for pricing equity-linked securities. J. Korean Soc. Ind. Appl. Math. 24 (2020), no. 1, 79-84.   DOI
6 D.R. Jeong, I.S. Wee & J.S. Kim: An operator splitting method for pricing the ELS option. J. Korean Soc. Ind. Appl. Math. 14 (2010), no. 3, 175-187.   DOI
7 Y. Kim, H.O. Bae & H.K. Koo: Option pricing and Greeks via a moving least square meshfree method. Quant. Finance 14 (2014), no. 10, 1753-1764.   DOI
8 C. Lee, J. Lyu, E. Park, W. Lee, S. Kim, D. Jeong & J. Kim: Super-Fast computation for the three-asset equity-linked securities using the finite difference method. Math. 8 (2020), no. 3, 307:1-13.
9 J. Persson & L. von Persson: Pricing European multi-asset options using a space-time adaptive FD-method. Comput. Vis. Sci. 10 (2007), no. 4, 173-183.   DOI
10 F. Soleymani: Efficient semi-discretization techniques for pricing European and American basket options. Comput. Econ. 53 (2019), no. 4, 1487-1508.   DOI
11 B. Dring, M. Fourni & Heuer, C: High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. J. Comput. Appl. Math. 271 (2014), 247-266.   DOI
12 F. Soleymani & A. Akgl: Improved numerical solution of multi-asset option pricing problem: A localized RBF-FD approach. Chaos, Solitons & Fractals. 119 (2019), 298-309.   DOI
13 J. Wang, Y. Yan, W. Chen, W. Shao & W. Tang: Equity-linked securities option pricing by fractional Brownian motion. Chaos, Solitons & Fractals 144 (2021), 110716.   DOI
14 M. Yoo, D. Jeong, S. Seo & J. Kim: A comparison study of explicit and implicit numerical methods for the equity-linked securities. Honam Math. J. 37 (2015), no. 4, 441-455.   DOI
15 J. Kim, T. Kim, J. Jo, Y. Choi, S. Lee, H. Hwang, M. Yoo, & D. Jeong: A practical finite difference method for the three-dimensional Black-Scholes equation. Eur. J. Oper. Res. 252 (2016), no. 1, 183-190.   DOI
16 Y. Kwon & Y. Lee: A second-order finite difference method for option pricing under jump-diffusion models. SIAM J. Numer. Anal. 49 (2011), no. 6, 2598-2617.   DOI
17 C. Reisinger & G. Wittum: On multigrid for anisotropic equations and variational inequalities pricing multi-dimensional European and American options. Comput. Vis. Sci. 7 (2004), no. 3-4, 189-197.   DOI
18 D.J. Duffy: Finite difference methods in financial engineering: a partial differential equation approach. John Wiley and Sons, New York, 2013.
19 S. Ikonen & J. Toivanen: Operator splitting methods for American option pricing. Appl. Math. Lett. 17 (2004), no. 7, 809-814.   DOI
20 D. Jeong & J. Kim: A comparison study of ADI and operator splitting methods on option pricing models. J. Comput. Appl. Math. 247 (2013), 162-171.   DOI
21 L. Li & G. Zhang: Error analysis of finite difference and Markov chain approximations for option pricing. Math. Finan. 28 (2018), no. 3, 877-919.   DOI
22 N. Rambeerich, D.Y. Tangman, M.R. Lollchund & M. Bhuruth: High-order computational methods for option valuation under multifactor models. Eur. J. Oper. Res. 224 (2013), no. 1, 219-226.   DOI
23 J. Wang, J. Ban, J. Han, S. Lee & D. Jeong: Mobile platform for pricing of equity-linked securities. J. Korean Soc. Ind. Appl. Math. 21 (2017), no. 3, 181-202.   DOI