Super-Fast computation for the three-asset equity-linked securities using the finite difference method

Chaeyoung Lee; Jisang Lyu; Eunchae Park; Wonjin Lee; Sangkwon Kim; Darae Jeong; Junseok Kim

doi:10.3390/math8030307

Super-Fast computation for the three-asset equity-linked securities using the finite difference method

Chaeyoung Lee, Jisang Lyu, Eunchae Park, Wonjin Lee, Sangkwon Kim, Darae Jeong, Junseok Kim

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one-and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.

Original language	English
Article number	307
Journal	Mathematics
Volume	8
Issue number	3
DOIs	https://doi.org/10.3390/math8030307
Publication status	Published - 2020 Mar 1

Bibliographical note

Funding Information:
Funding: The corresponding author (Junseok Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea.

Publisher Copyright:
© 2020 by the authors.

Keywords

Black-scholes equations
Equity-linked securities
Finite difference method
Super-fast computation

ASJC Scopus subject areas

General Mathematics

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10.3390/math8030307

Cite this

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title = "Super-Fast computation for the three-asset equity-linked securities using the finite difference method",

abstract = "In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one-and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.",

keywords = "Black-scholes equations, Equity-linked securities, Finite difference method, Super-fast computation",

author = "Chaeyoung Lee and Jisang Lyu and Eunchae Park and Wonjin Lee and Sangkwon Kim and Darae Jeong and Junseok Kim",

note = "Funding Information: Funding: The corresponding author (Junseok Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea. Publisher Copyright: {\textcopyright} 2020 by the authors.",

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AU - Lee, Chaeyoung

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AU - Park, Eunchae

AU - Lee, Wonjin

AU - Kim, Sangkwon

AU - Jeong, Darae

AU - Kim, Junseok

N1 - Funding Information: Funding: The corresponding author (Junseok Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea. Publisher Copyright: © 2020 by the authors.

PY - 2020/3/1

Y1 - 2020/3/1

N2 - In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one-and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.

AB - In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one-and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.

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ER -

Super-Fast computation for the three-asset equity-linked securities using the finite difference method

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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