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

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  • 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.

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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).
    11. 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.
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    Cited by:

    1. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    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.

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