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Equity-linked securities option pricing by fractional Brownian motion

Author

Listed:
  • Wang, Jian
  • Yan, Yan
  • Chen, Wenbing
  • Shao, Wei
  • Wang, Jian
  • Tang, Weiwei

Abstract

In this paper, we use the Monte Carlo simulation (MCS) method to price the Equity-Linked Securities (ELS) option by fractional Brownian motion (fBm). We use the fBm that satisfy the Itô process instead of the geometric Brownian motion, and we call the proposed model ELS-fBm model. We first do the convergence test with the number of MCS. Then, we price the one-, two-, and three-asset ELS by employing the classical ELS model and the ELS-fBm model, respectively. We see that the price of ELS varies with different Hurst exponent, which indicates that the ELS pricing model considering the long-range dependence is necessary and more suitable for the financial market under uncertain environment. In addition, we prove the superiority of our proposed model with an actual three-assets ELS product which is issued by Future Asset company. We find the ELS price calculated by the proposed ELS-fBm model almost the same as the ELS price in the ELS product contract issued by Future Asset company, while the classical ELS model produces a great deviation.

Suggested Citation

  • Wang, Jian & Yan, Yan & Chen, Wenbing & Shao, Wei & Wang, Jian & Tang, Weiwei, 2021. "Equity-linked securities option pricing by fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000692
    DOI: 10.1016/j.chaos.2021.110716
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    References listed on IDEAS

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    Cited by:

    1. Wang, Jian & Wen, Shuai & Yang, Mengdie & Shao, Wei, 2022. "Practical finite difference method for solving multi-dimensional black-Scholes model in fractal market," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Gómez-Águila, A. & Sánchez-Granero, M.A., 2021. "A theoretical framework for the TTA algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    3. Soobin Kwak & Youngjin Hwang & Yongho Choi & Jian Wang & Sangkwon Kim & Junseok Kim, 2022. "Reconstructing the Local Volatility Surface from Market Option Prices," Mathematics, MDPI, vol. 10(14), pages 1-12, July.
    4. Wang, Jian & Yang, Mengdie & Lu, Lin & Shao, Wei, 2022. "Does the “Delta Variant” affect the nonlinear dynamic characteristics of SARS-CoV-2 transmission?," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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    Keywords

    ELS; fBm; MCS; Hurst exponent;
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