IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4689-d1282789.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4689/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4689/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    7. 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.
    8. 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.
    9. Tsvetelin S. Zaevski, 2022. "Pricing cancellable American put options on the finite time horizon," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1284-1303, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Indu Rani & Chandan Kumar Verma, 2024. "Analyzing Short-Rate Models for Efficient Bond Option Pricing: A Review," SN Operations Research Forum, Springer, vol. 5(3), pages 1-26, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    2. Kensuke Kato & Nobuhiro Nakamura, 2024. "PDE-Based Bayesian Inference of CEV Dynamics for Credit Risk in Stock Prices," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 31(2), pages 389-421, June.
    3. Ramaprasad Bhar, 2010. "Stochastic Filtering with Applications in Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736.
    4. Bahadursingh, Roman, 2024. "Portfolio Management Using the Complex Wishart Distribution," Thesis Commons ma2hx_v1, Center for Open Science.
    5. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    6. repec:wyi:journl:002109 is not listed on IDEAS
    7. Jonathan A. Batten & Karren Lee-Hwei Khaw & Martin R. Young, 2014. "Convertible Bond Pricing Models," Journal of Economic Surveys, Wiley Blackwell, vol. 28(5), pages 775-803, December.
    8. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.
    9. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.
    10. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    11. Yu, Jun, 2014. "Econometric Analysis Of Continuous Time Models: A Survey Of Peter Phillips’S Work And Some New Results," Econometric Theory, Cambridge University Press, vol. 30(4), pages 737-774, August.
    12. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    13. repec:uts:finphd:40 is not listed on IDEAS
    14. Wang, Xiaohu & Phillips, Peter C.B. & Yu, Jun, 2011. "Bias in estimating multivariate and univariate diffusions," Journal of Econometrics, Elsevier, vol. 161(2), pages 228-245, April.
    15. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    16. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    17. Koo, Bonsoo & Linton, Oliver, 2012. "Estimation of semiparametric locally stationary diffusion models," Journal of Econometrics, Elsevier, vol. 170(1), pages 210-233.
    18. repec:wyi:journl:002108 is not listed on IDEAS
    19. Duffee, Gregory R., 1996. "On measuring credit risks of derivative instruments," Journal of Banking & Finance, Elsevier, vol. 20(5), pages 805-833, June.
    20. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    21. Muteba Mwamba, John & Thabo, Lethaba & Uwilingiye, Josine, 2014. "Modelling the short-term interest rate with stochastic differential equation in continuous time: linear and nonlinear models," MPRA Paper 64386, University Library of Munich, Germany.
    22. Broze, Laurence & Scaillet, Olivier & Zakoian, Jean-Michel, 1995. "Testing for continuous-time models of the short-term interest rate," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 199-223, September.
    23. Dette, Holger & Podolskij, Mark, 2008. "Testing the parametric form of the volatility in continuous time diffusion models--a stochastic process approach," Journal of Econometrics, Elsevier, vol. 143(1), pages 56-73, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4689-:d:1282789. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.