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An Integrated Model for Hybrid Securities

Author

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  • Sanjiv R. Das

    (Leavey School of Business, Santa Clara University, Santa Clara, California 95053)

  • Rangarajan K. Sundaram

    (Department of Finance, Stern School of Business, New York University, New York, New York 10012)

Abstract

We develop a model for pricing securities whose value may depend simultaneously on equity, interest-rate, and default risks. The framework may also be used to extract probabilities of default (PD) functions from market data. Our approach is entirely based on observables such as equity prices and interest rates, rather than on unobservable processes such as firm value. The model stitches together in an arbitrage-free setting a constant elasticity of variance (CEV) equity model (to represent the behavior of equity prices prior to default), a default intensity process, and a Heath-Jarrow-Morton (HJM) model for the evolution of riskless interest rates. The model captures several stylized features such as a negative relation between equity prices and equity volatility, a negative relation between default intensity and equity prices, and a positive relationship between default intensity and equity volatility. We embed the model on a discrete-time, recombining lattice, making implementation feasible with polynomial complexity. We demonstrate the simplicity of calibrating the model to market data and of using it to extract default information. The framework is extensible to handling correlated default risk and may be used to value distressed convertible bonds, debt-equity swaps, and credit portfolio products such as collateralized debt obligations (CDOs). Applied to the CDX INDU (credit default index-industrials) Index, we find the S& P 500 index explains credit premia.

Suggested Citation

  • Sanjiv R. Das & Rangarajan K. Sundaram, 2007. "An Integrated Model for Hybrid Securities," Management Science, INFORMS, vol. 53(9), pages 1439-1451, September.
    • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:9:p:1439-1451
    DOI: 10.1287/mnsc.1070.0702
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    5. Mateti, Ravi S. & Hegde, Shantaram P. & Puri, Tribhuvan, 2013. "Pricing securities with multiple risks: A case of exchangeable debt," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 1018-1028.
    6. Kirkby, J. Lars, 2023. "Hybrid equity swap, cap, and floor pricing under stochastic interest by Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(2), pages 961-978.
    7. Brian J. Henderson & Heather Tookes, 2012. "Do Investment Banks' Relationships with Investors Impact Pricing? The Case of Convertible Bond Issues," Management Science, INFORMS, vol. 58(12), pages 2272-2291, December.
    8. Nick Georgiopoulos, 2020. "Liability-driven investments of life insurers under investment credit risk," Risk Management, Palgrave Macmillan, vol. 22(2), pages 83-107, June.
    9. Jarno Talponen & Minna Turunen, 2022. "Option pricing: a yet simpler approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 57-81, June.
    10. Fan, Chenxi & Luo, Xingguo & Wu, Qingbiao, 2017. "Stochastic volatility vs. jump diffusions: Evidence from the Chinese convertible bond market," International Review of Economics & Finance, Elsevier, vol. 49(C), pages 1-16.
    11. 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.
    12. Das, Sanjiv R. & Hanouna, Paul, 2009. "Implied recovery," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1837-1857, November.
    13. Kalimipalli, Madhu & Nayak, Subhankar, 2012. "Idiosyncratic volatility vs. liquidity? Evidence from the US corporate bond market," Journal of Financial Intermediation, Elsevier, vol. 21(2), pages 217-242.
    14. Das, Sanjiv R. & Kim, Seoyoung, 2015. "Credit spreads with dynamic debt," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 121-140.
    15. Kalimipalli, Madhu & Nayak, Subhankar & Perez, M. Fabricio, 2013. "Dynamic effects of idiosyncratic volatility and liquidity on corporate bond spreads," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2969-2990.
    16. Jarno Talponen & Minna Turunen, 2017. "Option pricing: A yet simpler approach," Papers 1705.00212, arXiv.org, revised Mar 2018.
    17. Anjiao Wang, 2020. "The Pricing of Total Return Swap Under Default Contagion Models with Jump-Diffusion Interest Rate Risk," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 361-373, March.
    18. Zimmermann, Paul, 2021. "The role of the leverage effect in the price discovery process of credit markets," Journal of Economic Dynamics and Control, Elsevier, vol. 122(C).
    19. Emilio Barucci & Luca Del Viva, 2013. "Dynamic capital structure and the contingent capital option," Annals of Finance, Springer, vol. 9(3), pages 337-364, August.
    20. Heather Tookes & Brian Henderson, 2010. "Do Investment Banks' Relationships with Investors Impact Pricing? The Case of Convertible Bond Issues," Yale School of Management Working Papers amz2667, Yale School of Management.

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