Credit Risk Modeling Using Time-Changed Brownian Motion
AbstractMotivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard first passage problem for stochastic processes to capitalize on this time change structure and find that the distribution functions of such "first passage times of the second kind" are efficiently computable in a wide range of useful examples. Thus this new notion of first passage can be used to define the time of default in generalized structural credit models. Formulas for defaultable bonds and credit default swaps are given that are both efficiently computable and lead to realistic spread curves. Finally, we show that by treating joint firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.
Volume (Year): 12 (2009)
Issue (Month): 08 ()
Contact details of provider:
Web page: http://www.worldscinet.com/ijtaf/ijtaf.shtml
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Hieber, Peter & Scherer, Matthias, 2012. "A note on first-passage times of continuously time-changed Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 165-172.
- Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," DiMaD Working Papers 2012-02, Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze.
- Thomas R. Hurd & Zhuowei Zhou, 2011. "Two-factor capital structure models for equity and credit," Papers 1110.5846, arXiv.org.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim).
If references are entirely missing, you can add them using this form.