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 and Junseok Kim
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Chaeyoung Lee: Department of Mathematics, Korea University, Seoul 02841, Korea
Jisang Lyu: Department of Mathematics, Korea University, Seoul 02841, Korea
Eunchae Park: Department of Mathematics, Korea University, Seoul 02841, Korea
Wonjin Lee: Department of Financial Engineering, Korea University, Seoul 02841, Korea
Sangkwon Kim: Department of Mathematics, Korea University, Seoul 02841, Korea
Darae Jeong: Department of Mathematics, Kangwon National University, Gangwon-do 24341, Korea
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Korea

Mathematics, 2020, vol. 8, issue 3, 1-13

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: super-fast computation; Equity-linked securities; Black–Scholes equations; finite difference method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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