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Two-factor capital structure models for equity and credit

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  • Thomas R. Hurd
  • Zhuowei Zhou
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    Abstract

    We extend the now classic structural credit modeling approach of Black and Cox to a class of "two-factor" models that unify equity securities such as options written on the stock price, and credit products like bonds and credit default swaps. In our approach, the two sides of the stylized balance sheet of a firm, namely the asset value and debt value, are assumed to follow a two dimensional Markov process. Amongst models of this type we find examples that lead to derivative pricing formulas that are capable of reproducing the main features of well known equity models such as the variance gamma model, and at the same time reproducing the stylized facts about default stemming from structural models of credit risk. Moreover, in contrast to one-factor structural models, these models allow for much more flexible dependence between equity and credit markets. Two main technical obstacles to efficient implementation of these pricing formulas are overcome in our paper. The first obstacle stems from the barrier condition implied by the non-default of the firm, and is overcome by the idea of time-changing Brownian motion in a way that preserves the reflection principle for Brownian motion. The second obstacle is the difficulty of computing spread options: this is overcome by using results in recent papers that make efficient use of the two dimensional Fast Fourier Transform.

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    File URL: http://arxiv.org/pdf/1110.5846
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    Paper provided by arXiv.org in its series Papers with number 1110.5846.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.5846

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    1. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, American Finance Association, vol. 31(2), pages 351-67, May.
    2. T. R. Hurd, 2009. "Credit risk modeling using time-changed Brownian motion," Papers 0904.2376, arXiv.org.
    3. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 50(1), pages 53-85, March.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, American Finance Association, vol. 29(2), pages 449-70, May.
    5. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, Econometric Society, vol. 69(3), pages 633-64, May.
    6. Hayne E. Leland and Klaus Bjerre Toft., 1995. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Research Program in Finance Working Papers, University of California at Berkeley RPF-259, University of California at Berkeley.
    7. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, Springer, vol. 10(3), pages 303-330, September.
    8. T. R. Hurd, 2009. "Credit Risk Modeling Using Time-Changed Brownian Motion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 12(08), pages 1213-1230.
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