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Research Papers

An extended likelihood framework for modelling discretely observed credit rating transitions

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Pages 93-104 | Received 25 May 2017, Accepted 27 Mar 2018, Published online: 07 Jun 2018

References

  • Albert, A. , Estimating the infinitesimal generator of a continuous-time, finite state markov process. Ann. Math. Stat. , 1962, 33 , 727–753.
  • Bäck, T. and Schwefel, H.P. , Evolutionary computation: An overview. In Proceedings of IEEE International Conference on Evolutionary Computation , pp. 20–29, 1996 (Piscataway, NJ).
  • Billingsley, P. , Statistical methods in Markov chains. Ann. Math. Stat. , 1961, 32 , 12–40.
  • Blackwell, P.G. , Bayesian inference for Markov processes with diffusion and discrete components. Biometrika , 2003, 90 , 613–627.
  • Bladt, M. and Sørensen, M. , Statistical inference for discretely observed Markov jump processes. J. Roy. Stat. Soc. B , 2005, 67 , 395–410.
  • Bladt, M. and Sørensen, M. , Efficient estimation of transition rates between credit ratings from observations at discrete time points. Quant. Finance , 2009, 9 , 147–160.
  • Bluhm, C. and Wagner, C. , Valuation and risk management of collateralized debt obligations and related securities. Annu. Rev. Financ. Econ. , 2011, 3 , 193–222.
  • Couderc, F. , Credit risk and ratings: Understanding dynamics and relationships with macroeconomics. PhD Thesis, EPFL Lausanne, 2008.
  • Cuthbert, J.R. , On Uniqueness of the logarithm for Markov semi-groups. J. London Math. Soc. , 1972, 2 , 623–630.
  • Cuthbert, J.R. , The logarithm function for finite-state Markov semi-groups. J. London Math. Soc. , 1973, 2 , 524–532.
  • Delyon, B. , Lavielle, M. and Moulines, E. , Convergence of a stochastic monotone approximation of the EM algorithm. Ann. Stat. , 1999, 27 , 94–128.
  • Dempster, A.P. , Laird, N.M. and Rubin, D.B. , Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. B , 1977, 39 , 1–38.
  • Elfving, G. , Zur Theorie der Markoffschen Ketten. Acta Soc. Sci. Fenn. 1937, A.2 , 1–17.
  • Ethier, S.N. and Kurtz, T.G. , Markov Processes: Characterization and Convergence , 2005 (Wiley: Hoboken, NJ).
  • Fearnhead, P. and Sherlock, C. , An exact Gibbs sampler for the Markov-modulated Poisson process. J. Roy. Stat. Soc. B , 2006, 68 , 767–784.
  • Glaz, J. and Sison, C. , Simultaneous confidence intervals for multinomial proportions. J. Stat. Plan. Inference , 1999, 82 , 251–262.
  • Hanson, S. and Schuermann, T. , Confidence intervals for probabilities of default. J. Bank. Finance , 2006, 30 , 2281–2301.
  • Hobolth, A. , A Markov Chain Monte Carlo expectation maximization algorithm for statistical analysis of DNA sequence evolution with neighbor-dependent substitution rates. J. Comput. Graph. Stat. , 2008, 17 , 1–25.
  • Hobolth, A. and Stone, E.A. , Simulation from endpoint-conditioned, continuous-time Markov chains on a finite state space, with applications to molecular evolution. Ann. Appl. Stat. , 2009, 3 , 1204–1231.
  • Hughes, M. and Werner, R. , Choosing Markovian credit migration matrices by nonlinar optimization. Risks , 2016, 4 , 31.
  • Inamura, Y. , Estimating continuous time transition matrices from discretely observed data, 2006. Available online at: https://www.boj.or.jp/en/research/wps_rev/wps_2006/data/wp06e07.pdf.
  • Israel, R.B. , Rosenthal, J.S. and Wei, J.Z. , Finding generators for Markov chains via empirical transition matrices, with applications to credit ratings. Math. Finance , 2001, 11 , 245–265.
  • Jensen, A. , Markoff chains as an aid in the study of Markoff processes. Scand. Actuarial J. , 1953, 1953 , 87–91.
  • Kirkpatrick, S. , Gelatt, C.D. and Vecchi, M.P. , Optimization by simulated annealing. Science , 1983, 220 , 671–680.
  • Kreinin, E. and Sidelnikova, M. , Regularization algorithms for transition matrices. Algo Res. Q. , 2001, 4 , 23–40.
  • Kremer, A. and Weißbach, R. , Consistent estimation for discretely observed Markov jump processes with an absorbing state. Stat. Pap. , 2013, 54 , 993–1007.
  • Küchenhoff, H. and Buchberger, R. , Deriving an economic reasonable transition matrix using adjusted generator matrices. Technical Report, University of Munich, 2008.
  • Lavielle, M. and Moulines, E. , On a stochastic approximation version of the EM algorithm. Technical Report, Université Paris-Sud, 1995.
  • Lavielle, M. and Moulines, E. , A simulated annealing version of the EM algorithm for non-Gaussian deconvolution. Stat. Comput. , 1997, 7 , 229–236.
  • Levin, B. , A Representation for multinomial cumulative distribution functions. Ann. Stat. , 1981, 9 , 1123–1126.
  • Marshall, G. and Jones, R.H. , Multi-state models and diabetic retinopathy. Stat. Med. , 1995, 14 , 1975–1983.
  • Nielsen, R. , Mapping mutations on phylogenies. Syst. Biol. , 2002, 51 , 729–739.
  • Norris, J.R. , Markov Chains , 1998 (Cambridge University Press: New York).
  • Oakes, D. , Direct Calculation of the information matrix via the EM algorithm. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) 1999, 61 , 479–482.
  • Pawitan, Y. , In All Likelihood: Statistical Modelling and Inference Using Likelihood , 2001 (Clarendon Press: Oxford).
  • Pfeuffer, M. , Generator matrix approximation based on discrete-time rating migration data. Master Thesis, Ludwig Maximilian University of Munich, 2016.
  • Pfeuffer, M. , ctmcd: An R package for estimating the parameters of a continuous-time Markov chain from discrete-time data. R Journal , 2017, 9 , 127–141.
  • Schuermann, T. , Credit migration matrices. In Encyclopedia of Quantitative Risk Analysis and Assessment , edited by E.L. Melnick, and B.S. Everitt , pp. 401–406, 2008 (Wiley: Chichester, West Sussex).
  • Singer, B. and Spilerman, S. , The representation of social processes by Markov models. Amer. J. Sociol. , 1976, 82 , 1–54.
  • Sison, C. and Glaz, J. , Confidence intervals and sample size determination for multinomial proportions. J. Amer. Stat. Assoc. , 1995, 90 , 366–369.
  • Smith, G. and dos Reis, G. , Robust and consistent estimation of generators in credit risk. Quant. Finance , 2017. Available online at: https://doi.org/10.1080/14697688.2017.1383627.
  • Standard and Poor’s , Global corporate default study and rating transitions, 2000--2016. Available online at: https://cerep.esma.europa.eu/cerep-web/statistics/transitionMatrice.xhtml.
  • Trück, S. and Rachev, S.T. , Rating Based Modeling of Credit Risk: Theory and Application of Migration Matrices , 2009 (Academic Press: London).
  • van Loan, C. , Computing integrals involving the matrix exponential. IEEE Trans. Automat. Controls , 1978, AC 23 , 395–404.

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