Two-factor capital structure models for equity and credit
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert A. Jarrow & Stuart M. Turnbull, 2008.
"Pricing Derivatives on Financial Securities Subject to Credit Risk,"
World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409
World Scientific Publishing Co. Pte. Ltd..
- Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
- Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
- 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 RPF-259, University of California at Berkeley.
- 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.
- Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- 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.
- T. R. Hurd, 2009. "Credit risk modeling using time-changed Brownian motion," Papers 0904.2376, arXiv.org.
- Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
- Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
- 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., vol. 12(08), pages 1213-1230. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1110.5846. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.