Pricing five-asset Equity-Linked Securities (ELS) with step-down and knock-in barrier conditions on Android platform

Junseok Kim; Juho Ma; Hyunho Shin; Hyundong Kim; Junseok Kim; Juho Ma; Hyunho Shin; Hyundong Kim

doi:10.3934/math.2025476

AIMS Mathematics

2025, Volume 10, Issue 5: 10452-10470. doi: 10.3934/math.2025476

Previous Article Next Article

Research article Special Issues

Pricing five-asset Equity-Linked Securities (ELS) with step-down and knock-in barrier conditions on Android platform

1.
Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
2.
Department of Mathematics and Physics, Gangneung-Wonju National University, Gangneung 25457, Republic of Korea

Received: 23 December 2024 Revised: 10 April 2025 Accepted: 25 April 2025 Published: 07 May 2025
MSC : 39A50, 60H35, 65C30, 65Y04, 65Y20, 91G20, 91G60

In this work, we propose a computational algorithm for calculating the fair price of five-asset Equity-Linked Securities under a step-down structure and a knock-in barrier condition. By using the Android platform, we implement a Monte Carlo simulation to accurately compute the fair price of Equity-Linked Securities with five-asset dynamics, which offers the advantage of location-independent pricing through mobile devices. We use the Cholesky decomposition to generate correlated random numbers based on the correlation matrix of the five underlying assets. To generate the discrete stock price paths, a discretized stochastic differential model is considered under the geometric Brownian motion assumption. The findings confirm the usefulness of the Monte Carlo simulation in pricing five-asset step-down Equity-Linked Securities derivatives and demonstrate the practicality of conducting advanced financial calculations on mobile devices. The implementation of this algorithm on the Android platform represents a significant advancement in the development of multi-asset Equity-Linked Securities, which offer the potential for higher coupon yields. Moreover, this research highlights the potential for further innovations in Fintech and suggests that the integration of technology has the capacity to improve the investment process by improving the accessibility and efficiency of financial tools.
- option pricing,
- Equity-Linked Security,
- multi-asset,
- Monte Carlo method,
- Android platform
Citation: Junseok Kim, Juho Ma, Hyunho Shin, Hyundong Kim. Pricing five-asset Equity-Linked Securities (ELS) with step-down and knock-in barrier conditions on Android platform[J]. AIMS Mathematics, 2025, 10(5): 10452-10470. doi: 10.3934/math.2025476

Related Papers:

Abstract

In this work, we propose a computational algorithm for calculating the fair price of five-asset Equity-Linked Securities under a step-down structure and a knock-in barrier condition. By using the Android platform, we implement a Monte Carlo simulation to accurately compute the fair price of Equity-Linked Securities with five-asset dynamics, which offers the advantage of location-independent pricing through mobile devices. We use the Cholesky decomposition to generate correlated random numbers based on the correlation matrix of the five underlying assets. To generate the discrete stock price paths, a discretized stochastic differential model is considered under the geometric Brownian motion assumption. The findings confirm the usefulness of the Monte Carlo simulation in pricing five-asset step-down Equity-Linked Securities derivatives and demonstrate the practicality of conducting advanced financial calculations on mobile devices. The implementation of this algorithm on the Android platform represents a significant advancement in the development of multi-asset Equity-Linked Securities, which offer the potential for higher coupon yields. Moreover, this research highlights the potential for further innovations in Fintech and suggests that the integration of technology has the capacity to improve the investment process by improving the accessibility and efficiency of financial tools.

References

[1]	H. Kim, S. Park, K. S. Moon, Markov regime-switching in pricing equity-linked securities: An empirical study for losses in HSCEI-linked products, Financ. Res. Lett., 76 (2025) 106929. https://doi.org/10.1016/j.frl.2025.106929 doi: 10.1016/j.frl.2025.106929
[2]	R. K. Maurya, D. Li, A. P. Singh, V. K. Singh, Numerical algorithm for a general fractional diffusion equation, Math. Comput. Simul., 223 (2024), 405–432. https://doi.org/10.1016/j.matcom.2024.04.018 doi: 10.1016/j.matcom.2024.04.018
[3]	A. P. Singh, P. Rajput, R. K. Maurya, V. K. Singh, High order stable numerical algorithms for generalized time-fractional deterministic and stochastic telegraph models, Comput. Appl. Math., 43 (2024), 401. https://doi.org/10.1007/s40314-024-02900-6 doi: 10.1007/s40314-024-02900-6
[4]	A. P. Singh, R. K. Maurya, V. K. Singh, Analysis of a robust implicit scheme for space-time fractional stochastic nonlinear diffusion wave model, Int. J. Comput. Math., 100 (2023), 1625–1645. https://doi.org/10.1080/00207160.2023.2207677 doi: 10.1080/00207160.2023.2207677
[5]	P. Roul, V. P. Goura, A compact finite difference scheme for fractional Black–Scholes option pricing model, Appl. Numer. Math., 166 (2021), 40–60. https://doi.org/10.1016/j.apnum.2021.03.017 doi: 10.1016/j.apnum.2021.03.017
[6]	J. Wang, Y. Yan, W. Chen, W. Shao, W. Tang, Equity-linked securities option pricing by fractional Brownian motion, Chaos Soliton. Fract., 144 (2021), 110716. https://doi.org/10.1016/j.chaos.2021.110716 doi: 10.1016/j.chaos.2021.110716
[7]	S. T. Kim, H. G. Kim, J. H. Kim, ELS pricing and hedging in a fractional Brownian motion environment, Chaos Soliton. Fract., 142 (2021), 110453. https://doi.org/10.1016/j.chaos.2020.110453 doi: 10.1016/j.chaos.2020.110453
[8]	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), 181–202. http://dx.doi.org/10.12941/jksiam.2017.21.181 doi: 10.12941/jksiam.2017.21.181
[9]	J. Kim, D. Jeong, H. Jang, H. Kim, Mobile APP for computing option price of the four-underlying asset step-down ELS, J. Korean Soc. Ind. Appl. Math., 4 (2022), 343–352. http://doi.org/10.12941/jksiam.2022.26.343 doi: 10.12941/jksiam.2022.26.343
[10]	H. Jang, H. Han, H. Park, W. Lee, J. Lyu, J. Park, et al., Android application for pricing two-and three-asset Equity-Linked Securities, J. Korean Soc. Ind. Appl. Math., 23 (2019), 237–251. http://doi.org/10.12941/jksiam.2019.23.237 doi: 10.12941/jksiam.2019.23.237
[11]	S. Kim, J. Lyu, W. Lee, E. Park, H. Jang, C. Lee, et al., A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate, Comput. Econ., 63 (2024), 2069–2086. https://doi.org/10.1007/s10614-023-10394-3 doi: 10.1007/s10614-023-10394-3
[12]	V. Podlozhnyuk, M. Harris, Monte carlo option pricing, CUDA SDK, (2008).
[13]	N. Stamatopoulos, D. J. Egger, Y. Sun, C. Zoufal, R. Iten, N. Shen, et al., Option pricing using quantum computers, Quantum, 4 (2020), 291. https://doi.org/10.22331/q-2020-07-06-291 doi: 10.22331/q-2020-07-06-291
[14]	H. Hwang, Y. Choi, S. Kwak, Y. Hwang, S. Kim, J. Kim, Efficient and accurate finite difference method for the four underlying asset ELS, Pure Appl. Math., 28 (2021), 329–341. https://doi.org/10.7468/jksmeb.2021.28.4.329 doi: 10.7468/jksmeb.2021.28.4.329
[15]	H. Jang, S. Kim, J. Han, S. Lee, J. Ban, H. Han, et al., Fast Monte Carlo simulation for pricing equity-linked securities, Comput. Econ., 56 (2020), 865–882. https://doi.org/10.1007/s10614-019-09947-2 doi: 10.1007/s10614-019-09947-2
[16]	C. Yoo, Y. Choi, S. Kim, S. Kwak, Y. Hwang, J. Kim, Fast Pricing of Four Asset Equity-Linked Securities Using Brownian Bridge, J. Korean Soc. Ind. Appl. Math., 25 (2021), 82–92. https://doi.org/10.12941/jksiam.2021.25.082 doi: 10.12941/jksiam.2021.25.082
[17]	H. Jang, H. Kim, S. Jo, H. Kim, S. Lee, J. Lee, et al., Fast ANDROID implementation of Monte Carlo simulation for pricing equity-linked securities, J. Korean Soc. Ind. Appl. Math., 24 (2020), 79–84. http://dx.doi.org/10.12941/jksiam.2020.24.079 doi: 10.12941/jksiam.2020.24.079
[18]	C. R. Johnson, Positive definite matrices, Am. Math. Mon., 77 (1970), 82–92. https://doi.org/10.1080/00029890.1970.11992465 doi: 10.1080/00029890.1970.11992465
[19]	P. Glasserman, Monte Carlo methods in financial engineering, New York: Springer., 53 (2004). https://doi.org/10.1007/978-0-387-21617-1 doi: 10.1007/978-0-387-21617-1
[20]	J. Wang, C. Liu, Generating multivariate mixture of normal distributions using a modified Cholesky decomposition, Proc. 38th Conf. Winter Simul., (2006). https://doi.org/10.1109/WSC.2006.323100 doi: 10.1109/WSC.2006.323100
[21]	T. Wang, Q. Huang, A new Newton method for convex optimization problems with singular Hessian matrices, AIMS Math., 8 (2023). 21161–21175. https://doi.org/10.3934/math.20231078 doi: 10.3934/math.20231078
[22]	J. Kim, D. Jeong, H. Jang, H. Kim, Mobile APP for computing option price of the four-underlying asset step-down ELS, J. Korean Soc. Ind. Appl. Math., 26 (2022), 343–352. http://doi.org/10.12941/jksiam.2022.26.343 doi: 10.12941/jksiam.2022.26.343

Reader Comments

Your name:*

Email:*
© 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)