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Valuing convertible bonds and the option to exchange bonds for stock

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  • Finnerty, John D.

Abstract

The value of a conventional convertible bond is the value of a straight bond plus the value of the option to exchange it for a specified number of shares of common stock. First, I develop a closed-form contingent-claims convertible bond valuation model that quantifies the value of the exchange option when the short-term riskless rate, the firm's credit spread, and its share price are stochastic. I model the firm's decision to force early conversion as a stopping time problem in which the firm forces conversion as soon as the conversion value reaches the forced conversion barrier. I empirically validate the model by comparing model and market prices for a sample of 148 corporate convertible bonds issued between 2006 and 2010. The average median and mean pricing errors are −0.18% and 0.21%, respectively, which are within the average bid–ask spread for convertible bonds during the sample period. I use the model to quantify the disruptive impact that the prohibition on short selling during the recent financial crisis had on convertible bond prices.

Suggested Citation

  • Finnerty, John D., 2015. "Valuing convertible bonds and the option to exchange bonds for stock," Journal of Corporate Finance, Elsevier, vol. 31(C), pages 91-115.
    • Handle: RePEc:eee:corfin:v:31:y:2015:i:c:p:91-115
    DOI: 10.1016/j.jcorpfin.2014.12.012
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    3. Feng, Yun & Huang, Bing-hua & Huang, Yu, 2016. "Valuing resettable convertible bonds: Based on path decomposing," Finance Research Letters, Elsevier, vol. 19(C), pages 279-290.
    4. Jenny Jing Wang & Jianfu Shen & Frederik Pretorius, 2023. "Valuing options to renew at future market value: the case of commercial property leases," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-35, December.
    5. Liang‐Chih Liu & Tian‐Shyr Dai & Lei Zhou & Hao‐Han Chang, 2022. "Analyzing interactive call, default, and conversion policies for corporate bonds," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1597-1638, August.
    6. Juan David González-Ruiz & Maria Isabel Acosta-García & Ramón Villa-García, 2021. "Financial Behaviour in a Mandatory Conversion Process: Empirical Evidence from Colombia," Global Business Review, International Management Institute, vol. 22(1), pages 69-84, February.
    7. Tian‐Shyr Dai & Chen‐Chiang Fan & Liang‐Chih Liu & Chuan‐Ju Wang & Jr‐Yan Wang, 2022. "A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(12), pages 2103-2134, December.
    8. Ling, Yu-Xiu & Xie, Chi & Wang, Gang-Jin, 2022. "Interconnectedness between convertible bonds and underlying stocks in the Chinese capital market: A multilayer network perspective," Emerging Markets Review, Elsevier, vol. 52(C).

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    More about this item

    Keywords

    Valuation; Convertible bond; Exchange option; Stopping time; Empirical validation;
    All these keywords.

    JEL classification:

    • C29 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Other
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G30 - Financial Economics - - Corporate Finance and Governance - - - General
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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