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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Chaeyoung Lee & Jisang Lyu & Eunchae Park & Wonjin Lee & Sangkwon Kim & Darae Jeong & Junseok Kim, 2020. "Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method," Mathematics, MDPI, vol. 8(3), pages 1-13, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:307-:d:325148
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    References listed on IDEAS

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