Stochastic evolution equations in portfolio credit modelling

SIAM Journal on Financial Mathematics

Volumn 2, Issue 1, 2011, Pages 627-664

  Bush, N ^a   Hambly, B M ^a   Haworth, H ^b   Jin, L ^a   Reisinger, C ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b Credit Suisse group   (Switzerland)

Author keywords

Collateralized debt obligations; Credit derivatives; Stochastic partial differential equations

Indexed keywords

EID: 84870859945     PISSN: None     EISSN: 1945497X     Source Type: Journal    
DOI: 10.1137/100796777     Document Type: Article

References (48)

1. D. Aldous Exchangeability and related topics in ́ecole d'́et'e de probabilit'es de Saint-Flour XIII - 1983 Lecture Notes in Math. 1117 Springer Berlin 1985 pp. 1-198.
2. A. Bain and D. Crisan Fundamentals of Stochastic Filtering Springer New York 2009.
3. E. Bayraktar and B. Yang Multi-scale time-changed birth processes for pricing multi-name credit derivatives Appl. Math. Finance 16 (2009) pp. 429-449.
4. F. Black and J. Cox Valuing corporate securities: Some effects of bond indenture provisions J. Finance 31 (1976) pp. 351-367.
5. D. Brigo A. Pallavicini and R. Torresetti Credit models and the crisis: Default cluster dynamics and the generalized Poisson loss model J. Credit Risk 6 (2011) pp. 39-81.
6. N. Bush Stochastic Evolution Equations and Portfolio Credit Modelling M.Sc. thesis University of Oxford Oxford UK 2007.
7. N. Bush B. M. Hambly H. Haworth L. Jin and C. Reisinger Stochastic Evolution Equations in Portfolio Credit Modelling with Applications to Exotic Credit Products http://arxiv.org/abs/1103. 4947 (2011).
8. J. Cariboni and W. Schoutens Pricing Credit Default Swaps under Levy Models UCS report 2004- 2007 K.U. Leuven Leuven Belgium 2004.
9. R. Carmona and S. Creṕey Particle methods for the estimation of credit portfolio loss distributions Int. J. Theor. Appl. Finance 13 (2010) pp. 577-602.
10. R. Carmona J.-P. Fouque and D. Vestal Interacting particle systems for the computation of rare credit portfolio losses Finance Stoch. 13 (2009) pp. 613-633.
11. M. Davis and J. Rodriguez Large portfolio credit risk modelling Int. J. Theor. Appl. Finance 10 (2007) pp. 653-678.
12. M. K. Deb I. M. Babuska and J. T. Oden Solution of stochastic partial differential equations using Galerkin finite element techniques Comput. Methods Appl. Mech. Engrg. 190 (2001) pp. 6359-6372.
13. G. Di Graziano and C. Rogers A dynamic approach to the modeling of correlation credit derivatives using Markov chains Int. J. Theor. Appl. Finance 12 (2009) pp. 45-62.
14. D. Duffie and D. Lando Term structure of credit spreads with incomplete accounting information Econometrica 69 (2001) pp. 633-664.
15. E. Errais K. Giesecke and L. R. Goldberg Affine point processes and portfolio credit risk SIAM J. Financial Math. 1 (2010) pp. 642-665.
16. S. N. Ethier and T. G. Kurtz Markov Processes: Characterization and Convergence Wiley New York 1986.
17. D. Filipovic L. Overbeck and T. Schmidt Dynamic CDO term structure modelling Math. Finance 21 (2011) pp. 53-71.
18. C. Finger V. Finkelstein G. Pan J. Lardy T. Thomas and J. Tierney CreditGrades Technical document RiskMetrics Group Inc. 2002.
19. J. Fouque B. Wignall and X. Zhou Modeling correlated defaults: First passage model under stochastic volatility J. Comput. Finance 11 (2008) pp. 43-78.
20. H. Haworth and C. Reisinger Modelling basket credit default swaps with default contagion J. Credit Risk 3 (2007) pp. 31-67.
21. D. J. Higham Mean-square and asymptotic stability of the stochastic theta method SIAM J. Numer. Anal. 38 (2000) pp. 753-769.
22. B. Hilberink and L. C. G. Rogers Optimal capital structure and endogenous default Finance Stoch. 6 (2002) pp. 237-263.
23. J. Hull M. Predescu and A. White The valuation of correlation-dependent credit derivatives using a structural model J. Credit Risk 6 (2010) pp. 99-132.
24. J. Hull and A. White Valuing credit default swaps II: Modeling default correlations J. Derivatives 8 (2001) pp. 12-22.
25. J. Hull and A. White Forwards and European options on CDO tranches J. Credit Risk 3 (2007) pp. 63-73.
26. S. Iyengar Hitting lines with two-dimensional Brownian motion SIAM J. Appl. Math. 45 (1985) pp. 983-989.
27. K. Jackson and W. Zhang Valuation of forward starting CDOs Int. J. Comput. Math. 86 (2009) pp. 955-963.
28. L. Jin Particle Systems and SPDEs with Application to Credit Modelling D. Phil. thesis University of Oxford Oxford UK 2010.
29. M. Joshi and A. Stacey Intensity gamma a new approach to pricing portfolio credit derivatives Risk Magazine July (2006).
30. N. V. Krylov A Wn 2 -theory of the Dirichlet problem for SPDEs in general smooth domains Probab. Theory Related Fields 98 (1994) pp. 389-421.
31. T. G. Kurtz and J. Xiong Particle representations for a class of non-linear SPDEs Stochastic Process. Appl. 83 (1999) pp. 103-126.
32. S. V. Lototsky Dirichlet problem for stochastic parabolic equations in smooth domains Stochastics Stochastics Rep. 68 (1999) pp. 145-175.
33. R. Merton On the pricing of corporate debt: The risk structure of interest rates J. Finance 29 (1974) pp. 449-470.
34. A. Metzler On the first passage problem for correlated Brownian motion Statist. Probab. Lett. 80 (2010) pp. 277-284.
35. A. Mortensen Semi-analytical valuation of basket credit derivatives in intensity-based models J. Derivatives 13 (2006) pp. 8-26.
36. D. O'Kane Modelling Single-Name and Multi-name Credit Derivatives Wiley Finance Chichester UK 2008.
37. E. Papageorgiou and R. Sircar Multiscale intensity models and name grouping for valuation of multiname credit derivatives Appl. Math. Finance 16 (2009) pp. 353-383.
38. D. M. Pooley K. R. Vetzal and P. A. Forsyth Remedies for non-smooth payoffs in option pricing J. Comput. Finance 6 (2003) pp. 25-40.
39. A. Quarteroni and A. Valli Numerical Approximation of Partial Differential Equations Springer Berlin 1997.
40. R. Rannacher Finite element solution of diffusion problems with irregular data Numer. Math. 43 (1984) pp. 309-327.
41. D. Revuz and M. Yor Continuous Martingales and Brownian Motion 3rd ed. Springer Berlin 2005.
42. P. J. Schǒnbucher Credit Derivative Pricing Models Wiley New York 2003.
43. P. J. Schǒnbucher Portfolio Losses and the Term Structure of Loss Transition Rates: A New Methodology for the Pricing of Portfolio Credit Derivatives Working paper 2005.
44. R. Sircar and T. Zariphopoulou Utility valuation of multiname credit derivatives and application to CDOs Quant. Finance 10 (2010) pp. 195-208.
45. O. Vasicek Probability of Loss on Loan Portfolio Technical report KMV Corporation San Francisco 1987.
46. C. Zhou A Jump-Diffusion Approach to Modelling Credit Risk and Valuing Defaultable Securities Federal Reserve Board Washington DC 1997.
47. C. Zhou The term structure of credit spreads with jump risk J. Bank. Finance 25 (2001) pp. 2015-2040.
48. C. Zhou An analysis of default correlations and multiple defaults Rev. Financ. Stud. 14 (2001) pp. 555- 576.