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Projection and Contraction Method for Pricing American Bond Options

Author

Listed:
  • Qi Zhang

    (School of Science, Shenyang University of Technology, Shenyang 110870, China)

  • Qi Wang

    (School of Science, Shenyang University of Technology, Shenyang 110870, China)

  • Ping Zuo

    (School of New Energy and Intelligent Networked Automobile, University of Sanya, Sanya 572022, China)

  • Hongbo Du

    (School of Science, Shenyang University of Technology, Shenyang 110870, China)

  • Fangfang Wu

    (School of Science, Shenyang University of Technology, Shenyang 110870, China)

Abstract

In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite difference method is adopted to discretize the simplified model, and an equivalent variational form is obtained. Based on the positive definiteness of the discretized matrix, a projection and contraction method (PCM) is adopted for the resulting discretized variational problem. Finally, numerical experiments highlight the effectiveness and performance of the proposed algorithm.

Suggested Citation

  • Qi Zhang & Qi Wang & Ping Zuo & Hongbo Du & Fangfang Wu, 2023. "Projection and Contraction Method for Pricing American Bond Options," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4689-:d:1282789
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    References listed on IDEAS

    as
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    2. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2021. "Macro risks and the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 141(2), pages 479-504.
    3. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Matthew Lorig & Natchanon Suaysom, 2022. "Options on bonds: implied volatilities from affine short-rate dynamics," Annals of Finance, Springer, vol. 18(2), pages 183-216, June.
    6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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