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Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge

Author

Listed:
  • Jang Hanbyeol

    (Department of Financial Engineering, Korea University, Seoul02841, Republic of Korea)

  • Wang Jian

    (Department of Mathematics, Korea University, Seoul02841, Republic of Korea)

  • Kim Junseok

    (Department of Mathematics, Korea University, Seoul02841, Republic of Korea)

Abstract

We develop a numerical algorithm for predicting prices and Greeks of equity-linked securities (ELS) with a knock-in barrier at any time over the total time period from issue date to maturity by using Monte Carlo simulation (MCS). The ELS is one of the most important financial derivatives in Korea. In the proposed algorithm, first we calculate the probability (0≤p≤1{0\leq p\leq 1}) that underlying asset price never hits the knock-in barrier up to the intermediate evaluation date. Second, we compute two option prices Vn⁢k{V_{nk}} and Vk{V_{k}}, where Vn⁢k{V_{nk}} is the option value which knock-in event does not occur and Vk{V_{k}} is the option value which knock-in event occurs. Finally, we predict the option value with a weighted average. We apply the proposed algorithm to two- and three-asset ELS. We provide the pseudo-numerical algorithm and computational results to demonstrate the usefulness of the proposed method.

Suggested Citation

  • Jang Hanbyeol & Wang Jian & Kim Junseok, 2019. "Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge," Monte Carlo Methods and Applications, De Gruyter, vol. 25(4), pages 291-305, December.
    • Handle: RePEc:bpj:mcmeap:v:25:y:2019:i:4:p:291-305:n:1
    DOI: 10.1515/mcma-2019-2048
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    References listed on IDEAS

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    1. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    2. Kim, Junseok & Kim, Taekkeun & Jo, Jaehyun & Choi, Yongho & Lee, Seunggyu & Hwang, Hyeongseok & Yoo, Minhyun & Jeong, Darae, 2016. "A practical finite difference method for the three-dimensional Black–Scholes equation," European Journal of Operational Research, Elsevier, vol. 252(1), pages 183-190.
    3. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    4. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    5. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
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