Defaultable options in a Markovian intensity model of credit risk

Mathematical Finance

Volumn 18, Issue 4, 2008, Pages 493-518

  Bielecki, Tomasz R ^a,d   Crépey, Stéphane ^b   Jeanblanc, Monique ^b   Rutkowski, Marek ^c  

^a ILLINOIS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITÉ D EVRY VAL D ESSONNE   (France)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

^d Illinois Institute of Technology   (United States)

Author keywords

American options; Convertible bonds; Defaultable options; Game options; Hedging; Pricing; Reflected BSDEs; Variational inequalities

Indexed keywords

EID: 52249113333     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/j.1467-9965.2008.00345.x     Document Type: Conference Paper

References (24)

1. Andersen, L., and L. Buffum (2004 Calibration and Implementation of Convertible Bond Models, J. Comput. Finance 7, 1 34.
2. Ayache, E., P. Forsyth, and K. Vetzal (2003 Valuation of Convertible Bonds with Credit Risk, J. Derivatives, 11, 9 29.
3. Bielecki, T. R., S. Crépey, M. Jeanblanc, and M. Rutkowski (Forthcoming Arbitrage Pricing of Defaultable Game Options with Applications to Convertible Bonds, Quantit. Finance.
4. Bielecki, T. R., S. Crépey, M. Jeanblanc, and M. Rutkowski (2007 Valuation of Basket Credit Derivatives in the Credit Migrations Environment, Handbook of Financial Engineering J. Birge and V. Linetsky, eds. Amsterdam: North Holland.
5. Bielecki, T. R., S. Crépey, M. Jeanblanc, and M. Rutkowski (2006a Valuation and Hedging of Defaultable Game Options in a Hazard Process Model (Submitted).
6. Bielecki, T. R., S. Crépey, M. Jeanblanc, and M. Rutkowski (2006b Convertible Bonds in a Defaultable Diffusion Model (Submitted).
7. Bielecki, T. R., and M. Rutkowski (2002 Credit Risk: Modeling, Valuation and Hedging, Berlin Heidelberg New York: Springer-Verlag.
8. Cherny, A., and A. Shiryaev (2002 Vector Stochastic Integrals and the Fundamental Theorems of Asset Pricing, Proceedings of the Steklov Institute of Mathematics 237, 6 49.
9. Crépey, S., and A. Matoussi (Forthcoming Reflected and Doubly Reflected BSDEs with Jumps: A Priori Estimates and Comparison Principle Submitted).
10. Crépey, S. Markovian Reflected and Doubly Reflected BSDEs in a Jump-Diffusion Setting with Regimes, Ann. Appl. Probab. (Submitted).
11. Cvitanić, J., and I. Karatzas (1996 Backward Stochastic Differential Equations with Reflection and Dynkin Games, Ann. Probab. 24, 2024 2056.
12. Delbaen, F., and W. Schachermayer (1997 The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes, Math. Annal. 312, 215 250.
13. Dellacherie, C., B. Maisonneuve, and P.-A. Meyer (1992 Probabilités et Potentiel, Chapitres XVII-XXIV, Paris: Hermann.
14. El Karoui, N., S. Peng, and M.-C. Quenez (1997 Backward Stochastic Differential Equations in Finance, Mathematical Finance 7, 1 71.
15. Ethier, H. J., and T. G. Kurtz (1986 Markov Processes. Characterization and Convergence, New York: Wiley.
16. Hamadène, S., and M. Hassani (2006 BSDEs with Two Reflecting Barriers Driven by a Brownian Motion and an Independent Poisson Noise and Related Dynkin Game, Electron. J. Probab. 11, 121 145.
17. Jacod, J. (2003 Calcul Stochastique et Problèmes de Martingales, Berlin, Heidelberg, New York: Springer.
18. Jacod, J., and A. N. Shiryaev (1979 Limit Theorems for Stochastic Processes, Berlin, Heidelberg, New York: Springer.
19. Kallsen, J., and C. Kühn (2005 Convertible Bonds: Financial Derivatives of Game Type, in Exotic Option Pricing and Advanced Lévy Models, A. Kyprianou, W. Schoutens, and P. Wilmott, eds., pp. 277 288, Chichester: Wiley.
20. Kifer, Y. (2000 Game Options, Finance Stochast. 4, 443 463.
21. Ma, J., and J. Yong (1999 Forward-Backward Stochastic Differential Equations and Their Applications, Lecture Notes in Mathematics 1702, Berlin, Heidelberg, New York: Springer.
22. Mansuy, R., and M. Yor (2005 Random Times and Enlargement of Filtrations in a Brownian Setting, Lecture Notes in Mathematics 1873, Berlin, Heidelberg, New York: Springer.
23. Nikeghbali, A., and M. Yor (2005 A Definition and Some Characteristic Properties of Pseudo-stopping Times, Ann. Probab. 33, 1804 1824.
24. Protter, P. E. (2004 Stochastic Integration and Differential Equations, 2nd edn., Berlin, Heidelberg, New York: Springer.