IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v541y2020ics0378437119318837.html
   My bibliography  Save this article

Merton’s equation and the quantum oscillator: Pricing risky corporate coupon bonds

Author

Listed:
  • Baaquie, Belal Ehsan

Abstract

Merton has proposed a model of the contingent claims on a firm as an option on the firms value, and the model is based on a generalization of the Black–Scholes stochastic equation. Merton’s model can be used to price any contingent claim on the firm. A risk-sharing oscillator model for the pricing of corporate coupon bonds is proposed that leads to stochastic coupons, with the dynamics of the contingent claims being determined by the quantum oscillator. The oscillator model allows for the exact derivation of many results using quantum mathematics. The price of the risk-sharing coupon bonds and the stochastic coupons is derived exactly using the Feynman path integral.

Suggested Citation

  • Baaquie, Belal Ehsan, 2020. "Merton’s equation and the quantum oscillator: Pricing risky corporate coupon bonds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318837
    DOI: 10.1016/j.physa.2019.123367
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119318837
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123367?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jones, E Philip & Mason, Scott P & Rosenfeld, Eric, 1984. "Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 611-625, July.
    2. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 541-552, November.
    3. Suresh Sundaresan, 2013. "A Review of Merton’s Model of the Firm’s Capital Structure with Its Wide Applications," Annual Review of Financial Economics, Annual Reviews, vol. 5(1), pages 21-41, November.
    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. Baaquie, Belal Ehsan, 2019. "Merton’s equation and the quantum oscillator II: Option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    6. Jan Ericsson & Joel Reneby, 2005. "Estimating Structural Bond Pricing Models," The Journal of Business, University of Chicago Press, vol. 78(2), pages 707-735, March.
    7. Merton, Robert C., 1977. "On the pricing of contingent claims and the Modigliani-Miller theorem," Journal of Financial Economics, Elsevier, vol. 5(2), pages 241-249, November.
    8. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    9. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    10. Baaquie, Belal Ehsan, 2018. "Bonds with index-linked stochastic coupons in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 148-169.
    11. Eberhart, Allan C., 2005. "A comparison of Merton's option pricing model of corporate debt valuation to the use of book values," Journal of Corporate Finance, Elsevier, vol. 11(1-2), pages 401-426, March.
    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. Belal Ehsan Baaquie & Muhammad Mahmudul Karim, 2024. "Corporate bonds: fixed versus stochastic coupons—an empirical study," Journal of Asset Management, Palgrave Macmillan, vol. 25(1), pages 113-128, February.
    2. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    3. Belal Ehsan Baaquie & Muhammad Mahmudul Karim, 2023. "Pricing risky corporate bonds: An empirical study," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(1), pages 90-121, January.

    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. Bougias, Alexandros & Episcopos, Athanasios & Leledakis, George N., 2022. "The role of asset payouts in the estimation of default barriers," International Review of Financial Analysis, Elsevier, vol. 81(C).
    2. Belal Ehsan Baaquie & Muhammad Mahmudul Karim, 2023. "Pricing risky corporate bonds: An empirical study," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(1), pages 90-121, January.
    3. 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.
    4. Robert Elliott & Jia Shen, 2015. "Dynamic optimal capital structure with regime switching," Annals of Finance, Springer, vol. 11(2), pages 199-220, May.
    5. Bruche, Max, 2005. "Estimating structural bond pricing models via simulated maximum likelihood," LSE Research Online Documents on Economics 24647, London School of Economics and Political Science, LSE Library.
    6. Jing-Zhi Huang & Zhan Shi & Hao Zhou, 2020. "Specification Analysis of Structural Credit Risk Models [Corporate bond valuation and hedging with stochastic interest rates and endogenous bankruptcy]," Review of Finance, European Finance Association, vol. 24(1), pages 45-98.
    7. Stephanie Heck, 2022. "Corporate bond yields and returns: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 36(2), pages 179-201, June.
    8. Afik, Zvika & Arad, Ohad & Galil, Koresh, 2016. "Using Merton model for default prediction: An empirical assessment of selected alternatives," Journal of Empirical Finance, Elsevier, vol. 35(C), pages 43-67.
    9. Gregory Connor & Lisa R. Goldberg & Robert A. Korajczyk, 2010. "Portfolio Risk Analysis," Economics Books, Princeton University Press, edition 1, number 9224.
    10. Max Bruche, 2006. "Estimating Structural Models of Corporate Bond Prices," Working Papers wp2006_0610, CEMFI.
    11. Vogl, Konstantin & Maltritz, Dominik & Huschens, Stefan & Karmann, Alexander, 2006. "Country Default Probabilities: Assessing and Backtesting," Dresden Discussion Paper Series in Economics 12/06, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    12. Li, Ka Leung & Wong, Hoi Ying, 2008. "Structural models of corporate bond pricing with maximum likelihood estimation," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 751-777, September.
    13. Abel Elizalde, 2006. "Credit Risk Models II: Structural Models," Working Papers wp2006_0606, CEMFI.
    14. Belal Ehsan Baaquie & Muhammad Mahmudul Karim, 2024. "Corporate bonds: fixed versus stochastic coupons—an empirical study," Journal of Asset Management, Palgrave Macmillan, vol. 25(1), pages 113-128, February.
    15. Forte, Santiago & Lovreta, Lidija, 2012. "Endogenizing exogenous default barrier models: The MM algorithm," Journal of Banking & Finance, Elsevier, vol. 36(6), pages 1639-1652.
    16. Correia, Ricardo & Población, Javier, 2015. "A structural model with Explicit Distress," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 112-130.
    17. Lara Cathcart & Lina El-Jahel, 2006. "Pricing defaultable bonds: a middle-way approach between structural and reduced-form models," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 243-253.
    18. Goldstein, Michael A. & Namin, Elmira Shekari, 2023. "Corporate bond liquidity and yield spreads: A review," Research in International Business and Finance, Elsevier, vol. 65(C).
    19. 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.
    20. Reisz, Alexander S. & Perlich, Claudia, 2007. "A market-based framework for bankruptcy prediction," Journal of Financial Stability, Elsevier, vol. 3(2), pages 85-131, July.

    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:eee:phsmap:v:541:y:2020:i:c:s0378437119318837. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.