Large portfolio asymptotics for loss from default

Mathematical Finance

Volumn 25, Issue 1, 2015, Pages 77-114

  Giesecke, Kay ^a   Spiliopoulos, Konstantinos ^b   Sowers, Richard B ^c   Sirignano, Justin A ^a  

^a STANFORD UNIVERSITY   (United States)

^b BOSTON UNIVERSITY   (United States)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Credit risk; Interacting point process; Law of large numbers

Indexed keywords

EID: 84920986954     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/mafi.12011     Document Type: Article

References (31)

1. Ang, D. D., R. Gorenflo, V. K. Le, and D. D. Trong (2002): Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction, Lecture Notes in Mathematics, Berlin: Springer-Verlag.
2. Azizpour, S., K. Giesecke, and G. Schwenkler (2010): Exploring the Sources of Default Clustering, Working Paper, Stanford University.
3. Beskos, A., and G. Roberts (2005): Exact Simulation of Diffusions, Ann. Appl. Probab. 15(4), 2422-2444.
4. Bush, N., B. Hambly, H. Haworth, L. Jin, and C. Reisinger (2011): Stochastic Evolution Equations in Portfolio Credit Modelling, SIAM J. Finan. Math. 2, 627-664.
5. Chen, N. (2013): Localization and Exact Simulation of Brownian Motion Driven Stochastic Differential Equations, Math. Operat. Res. 38(3), 591-616.
6. Cvitanić, J., J. Ma, and J. Zhang (2011): Law of Large Numbers for Self-Exciting Correlated Defaults, Stoch. Process. Appl. 122, 2781-2810.
7. Dai Pra, P., and M. Tolotti (2009): Heterogeneous Credit Portfolios and the Dynamics of the Aggregate Losses, Stoch. Process. Appl. 119, 2913-2944.
8. Dai Pra, P., W. Runggaldier, E. Sartori, and M. Tolotti (2009): Large Portfolio Losses: A Dynamic Contagion Model, Ann. Appl. Probab. 19, 347-394.
9. Das, S., D. Duffie, N. Kapadia, and L. Saita (2007): Common Failings: How Corporate Defaults Are Correlated, J. Finance 62, 93-117.
10. Davis, M., and J. C. E. Rodriguez (2007): Large Portfolio Credit Risk Modelling, Int. J. Theor. Appl. Finance 10, 653-678.
11. Dembo, A., J.-D. Deuschel, and D. Duffie (2004): Large Portfolio Losses, Finance Stoch. 8, 3-16.
12. Duffie, D., L. Saita, and K. Wang (2006): Multi-Period Corporate Default Prediction with Stochastic Covariates, J. Finan. Econ. 83(3), 635-665.
13. Ethier, S. N., and T. G. Kurtz (1986): Markov Processes: Characterization and Convergence, New York: John Wiley & Sons Inc.
14. Feller, W. (1951): Two Singular Diffusion Problems, Ann. Math. 54(1), 173-182.
15. Giesecke, K., and D. Smelov (2013): Exact Sampling of Jump-Diffusions, Operat. Res. 61(4), 894-907.
16. Giesecke, K., and G. Schwenkler (2011): Filtered Likelihood for Point Processes. Working Paper, Stanford University.
17. Giesecke, K., K. Spiliopoulos, and R. Sowers (2011): Default Clustering in Large Portfolios: Typical Events, Ann. Appl. Probab. Forthcoming.
18. Giesecke, K., and S. Weber (2006): Credit Contagion and Aggregate Losses, J. Econ. Dyn. Contl. 30, 741-767.
19. Glasserman, P., W. Kang, and P. Shahabuddin (2007): Large Deviations in Multifactor Portfolio Credit Risk, Math. Finance 17(3), 345-379.
20. Gordy, M. B. (2003): A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules, J. Finan. Inter. 12, 199-232.
21. 1, J. Theor. Probab. 21(1), 169-192.
22. Kim, K.-H. (2009): Sobolev Space Theory of SPDEs with Continuous or Measurable Leading Coefficients, Stoch. Process. Appl. 119(1), 16-44.
23. Krylov, N., and S. Lototsky (1998): A Sobolev Space Theory of SPDEs with Constant Coefficients on a Half Line, SIAM J. Math. Anal. 30(2), 298-325.
24. Lototsky, S. (2001): Linear Stochastic Parabolic Equations Degenerating on the Boundary of a Domain, Electr. J. Probab. 6(24), 1-14.
25. Lucas, A., P. Klaassen, P. Spreij, and S. Straetmans (2001): An Analytic Approach to Credit Risk of Large Corporate Bond and Loan Portfolios, J. Bank. Finance 25, 1635-1664.
26. Royden, H. (1988): Real Analysis, 3rd ed., New York: Macmillan Publishing Company.
27. Schloegl, L., and D. O'Kane (2005): A Note on the Large Homogeneous Portfolio Approximation with the Student-t Copula, Finance Stoch. 9(4), 577-584.
28. Sircar, R., and T. Zariphopoulou (2010): Utility Valuation of Credit Derivatives and Application to CDOs, Quantit. Finance 10(2), 195-208.
29. Vasicek, O. (1991): Limiting Loan Loss Probability Distribution, Technical Report, KMV Corporation.
30. Vincenti, W. G., and C. H. Kruger (1965): Introduction to Physical Gas Dynamics, New York: John Wiley & Sons.
31. Zhang, X., J. Blanchet, K. Giesecke, and P. Glynn (2011): Affine Point Processes: Asymptotic Analysis and Efficient Rare-Event Simulation, Working Paper, Stanford University.