Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method

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 financ...

Full description

Bibliographic Details
Main Authors:	Chaeyoung Lee, Jisang Lyu, Eunchae Park, Wonjin Lee, Sangkwon Kim, Darae Jeong, Junseok Kim
Format:	Article
Language:	English
Published:	MDPI AG 2020-02-01
Series:	Mathematics
Subjects:	super-fast computation equity-linked securities black–scholes equations finite difference method
Online Access:	https://www.mdpi.com/2227-7390/8/3/307

id	doaj-f6a5a60b49b34c439ac27d55dcafa012
record_format	Article
spelling	doaj-f6a5a60b49b34c439ac27d55dcafa0122020-11-25T01:55:07ZengMDPI AGMathematics2227-73902020-02-018330710.3390/math8030307math8030307Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference MethodChaeyoung Lee0Jisang Lyu1Eunchae Park2Wonjin Lee3Sangkwon Kim4Darae Jeong5Junseok Kim6Department of Mathematics, Korea University, Seoul 02841, KoreaDepartment of Mathematics, Korea University, Seoul 02841, KoreaDepartment of Mathematics, Korea University, Seoul 02841, KoreaDepartment of Financial Engineering, Korea University, Seoul 02841, KoreaDepartment of Mathematics, Korea University, Seoul 02841, KoreaDepartment of Mathematics, Kangwon National University, Gangwon-do 24341, KoreaDepartment of Mathematics, Korea University, Seoul 02841, KoreaIn 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.https://www.mdpi.com/2227-7390/8/3/307super-fast computationequity-linked securitiesblack–scholes equationsfinite difference method
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Chaeyoung Lee Jisang Lyu Eunchae Park Wonjin Lee Sangkwon Kim Darae Jeong Junseok Kim
spellingShingle	Chaeyoung Lee Jisang Lyu Eunchae Park Wonjin Lee Sangkwon Kim Darae Jeong Junseok Kim Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method Mathematics super-fast computation equity-linked securities black–scholes equations finite difference method
author_facet	Chaeyoung Lee Jisang Lyu Eunchae Park Wonjin Lee Sangkwon Kim Darae Jeong Junseok Kim
author_sort	Chaeyoung Lee
title	Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method
title_short	Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method
title_full	Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method
title_fullStr	Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method
title_full_unstemmed	Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method
title_sort	super-fast computation for the three-asset equity-linked securities using the finite difference method
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2020-02-01
description	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.
topic	super-fast computation equity-linked securities black–scholes equations finite difference method
url	https://www.mdpi.com/2227-7390/8/3/307
work_keys_str_mv	AT chaeyounglee superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod AT jisanglyu superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod AT eunchaepark superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod AT wonjinlee superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod AT sangkwonkim superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod AT daraejeong superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod AT junseokkim superfastcomputationforthethreeassetequitylinkedsecuritiesusingthefinitedifferencemethod
_version_	1724984925143171072

Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method

Similar Items