Application of nonlinear filtering to credit risk

Operations Research Letters

Volumn 38, Issue 6, 2010, Pages 527-532

  Borkar, Vivek S ^a   Ghosh, Mrinal K ^b   Rangarajan, G ^b  

^a TATA INSTITUTE OF FUNDAMENTAL RESEARCH   (India)

^b INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Asset; EM algorithm; Equity; Merton's model; Nonlinear filter

Indexed keywords

ASSET; EM ALGORITHMS; EQUITY; MERTON'S MODEL; NONLINEAR FILTER;

ALGORITHMS; NONLINEAR FILTERING; RISK ASSESSMENT;

MAXIMUM LIKELIHOOD ESTIMATION;

EID: 77958083543     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2010.08.013     Document Type: Article

References (31)

1. E. Bayraktar, B. Yang, A unified framework for pricing credit and equity derivatives, September, 2008 arXiv:0712.3617v2.
2. T.R. Bielecki, and M. Rutkowski Credit Risk: Modelling, Valuation and Hedging 2004 Springer Verlag Berlin-Heidelberg
3. F. Black, and J. Cox Valuing corporate securities: some effects of bond indenture provisions Journal of Finance 31 1976 351 367
4. F. Black, and M. Scholes The pricing of options and corporate liabilities Journal of Political Economy 81 1973 637 659
5. C. Bluhm, L. Overbeck, and C. Wagner An Introduction to Credit Risk Modelling 2003 Chapman and Hall / CRC London
6. V.S. Borkar Optimal Control of Diffusion Processes, Pitman Research Notes in Mathematics no. 209 1989 Longman Scientific and Technical Harlow, UK
7. V.S. Borkar, K. Sureshkumar, McKeanVlasov limit in portfolio optimization, Stochastic Anal. Appl. (2010) (in press).
8. M. Crouhy, D. Galai, R. Mark, Credit risk revisited, Credit Risk Supplement, March, 1998, pp. 4044.
9. I. Csiszar, and P.C. Shields Information theory and statistics: a tutorial Foundations and Trends in Communications and Information Theory 1 2004 417 528
10. I. Csiszar, and G. Tusnady Information geometry and alternating minimization procedure Statistics and Decisions Supplement Issue No. 1 1984 205 237
11. M.H.A. Davis Pathwise nonlinear filtering, in stochastic systems: the mathematics of filtering and identification and applications M. Hazewinkel, J.C. Willems, NATO Advanced Study Institute Series 1981 D. Reidel Dordrecht 505 528
12. P. Del Moral Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems The Annals of Applied Probability 8 1998 438 495
13. D. Duffie, and L. Lando The term structure of credit spreads with incomplete accounting information Econometrica 69 2001 633 664
14. D. Duffie, and K.J. Singleton Credit Risk 2005 Princeton Uni. Press Princeton, N.J.
15. R. Geske The valuation of corporate liabilities as compound options Journal of Financial and Quantitative Analysis 5 1977 541 552
16. K. Giesecke Credit risk modelling and valuation: an introduction D. Shimko, Credit Risk: Models and Management vol. 2 2004 Riskbooks London
17. S. Haykin Adaptive Filter Theory 2002 Pearson Education Singapore
18. J. Hull, I. Nelken, A. White, Merton's model, credit risk and volatility skews, Working paper, 2006.
19. K. Ito, and B.L. Rozovskii Approximation of the Kushner equation of nonlinear filtering SIAM Journal of Control and Optimization 38 2000 893 915
20. J.C. Jackwirth, and M. Rubinstein Recovering probabilities from option prices Journal of Finance 51 1996 1611 1631
21. A.H. Jazwinski Stochastic Processes and Filtering Theory 1970 Academic Press New York
22. S. Kealhofer Managing default risk in portfolios of derivatives Derivative Credit Risk: Advances in Measurement and Management 1995 Risk Publications London 49 66
23. H.J. Kushner, and P. Dupuis Numerical Methods for Stochastic Control Problems in Continuous Time 2nd ed. 2001 Springer Verlag New York
24. H.E. Leland, and B.K. Toft Optimal capital structure, endogenous bankruptcy, and the term structure of credit spreads Journal of Finance 51 1996 987 1019
25. F.A. Longstaff, and E. Schwartz A simple approach to valuing risky fixed and floating debt Journal of Finance 50 1995 789 819
26. S. Lototsky, R. Mikulevicius, and B.L. Rozovskii Nonlinear filtering revisited: a spectral approach SIAM Journal of Control and Optimization 35 1997 435 461
27. R.M. Merton On the pricing of corporate debt: the risk structure of interest rate Journal of Finance 29 1974 449 470
28. R. Mikulevicius, and B.L. Rozovskii FourierHermite expansions for nonlinear filtering Theory of Probability and Applications 44 2000 606 612
29. N.I. Portenko Diffusion processes with unbounded drift coefficient Theory of Probability and Applications 20 1975 27 37
30. R.H. Shumway, and D.S. Stoffer Time Series Analysis and its Applications 2000 Springer New York
31. C. Yi, A. Tchernitser, T. Hurd, Randomized structural models of credit spreads, Working paper, June 2009.