Pricing and Semimartingale Representations of Vulnerable Contingent Claims in Regime-Switching Markets
Using a suitable change of probability measure, we obtain a novel Poisson series representation for the arbitrage- free price process of vulnerable contingent claims in a regime-switching market driven by an underlying continuous- time Markov process. As a result of this representation, along with a short-time asymptotic expansion of the claim's price process, we develop an efficient method for pricing claims whose payo?s may depend on the full path of the underlying Markov chain. The proposed approach is applied to price not only simple European claims such as defaultable bonds, but also a new type of path-dependent claims that we term self-decomposable, as well as the important class of vulnerable call and put options on a stock. We provide a detailed error analysis and illustrate the accuracy and computational complexity of our method on several market traded instruments, such as defaultable bond prices, barrier options, and vulnerable call options. Using again our Poisson series representation, we show differentiability in time of the pre-default price function of European vulnerable claims, which enables us to rigorously deduce Feynman-Kac representations for the pre-default pricing function and new semimartingale representations for the price process of the vulnerable claim under both risk-neutral and objective probability measures.
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.:
- Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc & Marek Rutkowski, 2008. "Arbitrage pricing of defaultable game options with applications to convertible bonds," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 795-810.
- Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
- Tomasz R. Bielecki & Stéphane Crépey & Monique Jeanblanc & Marek Rutkowski, 2008. "Defaultable Options In A Markovian Intensity Model Of Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 493-518.
- Tomasz Bielecki & Inwon Jang, 2006. "Portfolio optimization with a defaultable security," Asia-Pacific Financial Markets, Springer, vol. 13(2), pages 113-127, June.
- Ang, Andrew & Bekaert, Geert, 2002. "Short rate nonlinearities and regime switches," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1243-1274, July.
- Andrew Ang & Geert Bekaert, 1998.
"Regime Switches in Interest Rates,"
NBER Working Papers
6508, National Bureau of Economic Research, Inc.
- Christophette Blanchet-Scalliet & Monique Jeanblanc, 2004. "Hazard rate for credit risk and hedging defaultable contingent claims," Finance and Stochastics, Springer, vol. 8(1), pages 145-159, January.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:1110.0403. 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 references are entirely missing, you can add them using this form.