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Assessment of mortgage default risk via Bayesian state space models. (English) Zbl 1283.62211

Summary: Managing risk at the aggregate level is crucial for banks and financial institutions as required by the Basel III framework. we introduce discrete time Bayesian state space models with Poisson measurements to model aggregate mortgage default rates. We discuss parameter updating, filtering, smoothing, forecasting and estimation using Markov chain Monte Carlo methods. In addition, we investigate the dynamic behavior of the default rates and the effects of macroeconomic variables. We illustrate the use of the proposed models using actual U.S. residential mortgage data and discuss insights gained from Bayesian analysis.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62F15 Bayesian inference
65C40 Numerical analysis or methods applied to Markov chains
91B30 Risk theory, insurance (MSC2010)
65C60 Computational problems in statistics (MSC2010)

Software:

BayesDA
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References:

[1] Ambrose, B. W. and Capone, C. A. (1998). Modeling the conditional probability of foreclosure in the context of single-family mortgage default resolutions. Real Estate Economics 26 391-429.
[2] Chib, S. and Greenberg, E. (1995). Understanding the Metropolis-Hasting algorithm. Amer. Statist. 49 327-335.
[3] Cox, D. R. (1972). The statistical analysis of dependencies in point processes. In Stochastic Point Processes : Statistical Analysis , Theory , and Applications ( Conf. , IBM Res. Center , Yorktown Heights , NY , 1971) (P. A. W. Lewis, ed.) 55-66. Wiley, New York. · Zbl 0263.62058
[4] Cox, D. R. (1981). Statistical analysis of time series: Some recent developments. Scand. J. Stat. 8 93-115. · Zbl 0468.62079
[5] Frühwirth-Schnatter, S. (1994). Data augmentation and dynamic linear models. J. Time Series Anal. 15 183-202. · Zbl 0815.62065
[6] Gelfand, A. E. (1996). Model determination using sampling-based methods. In Markov Chain Monte Carlo in Practice 145-161. Chapman & Hall, London. · Zbl 0840.62003
[7] Gelfand, A. E., Dey, D. K. and Chang, H. (1992). Model determination using predictive distributions with implementation via sampling-based methods. In Bayesian Statistics , 4 ( Peñíscola , 1991) (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 147-167. Oxford Univ. Press, New York.
[8] Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (1995). Bayesian Data Analysis . Chapman & Hall, London. · Zbl 1279.62004
[9] Gilberto, S. M. and Houston, A. L. (1989). Relocation opportunities and mortgage default. AREUEA Journal 17 55-69.
[10] Herzog, T. N. (1988). Analyzing recent experience on FHA investor loans. Transactions of Society of Actuaries 40 405-421.
[11] Kass, R. E. and Raftery, A. E. (1995). Bayes factors. J. Amer. Statist. Assoc. 90 773-795. · Zbl 0846.62028
[12] Kau, J. B., Keenan, D. C., Muller-III, W. J. and Epperson, J. F. (1990). Pricing commercial mortgages and their mortgage backed securities. The Journal of Real Estate Finance and Economics 3 333-356.
[13] Kiefer, N. M. (2010). Default estimation and expert information. J. Bus. Econom. Statist. 28 320-328. · Zbl 1197.91193
[14] Kiefer, N. M. (2011). Default estimation, correlated defaults, and expert information. J. Appl. Econometrics 26 173-192.
[15] Lambrecht, B., Perraudin, W. and Satchell, S. (1997). Time to default in the UK mortgage market. Economic Modeling 14 485-499.
[16] Lambrecht, B., Perraudin, W. and Satchell, S. (2003). Mortgage default and possession under recourse: A competing hazards approach. Journal of Money , Credit and Banking 35 425-442.
[17] Leece, D. (2004). Economics of the Mortgage Market : Perspectives on Household Decision Making . Blackwell, Oxford.
[18] Morali, N. and Soyer, R. (2003). Optimal stopping in software testing. Naval Res. Logist. 50 88-104. · Zbl 1045.90018
[19] Popova, I., Popova, E. and George, E. I. (2008). Bayesian forecasting of prepayment rates for individual pools of mortgages. Bayesian Anal. 3 393-426. · Zbl 1330.62345
[20] Quercia, R. G. and Stegman, M. A. (1992). Residential mortgage default: A review of the literature. Journal of Housing Research 3 341-379.
[21] Santos, T. R. D., Gamerman, D. and Franco, G. C. (2012). A non-Gaussian family of state-space models with exact marginal likelihood. Technical report. · Zbl 1306.62196
[22] Smith, A. F. M. and Gelfand, A. E. (1992). Bayesian statistics without tears: A sampling-resampling perspective. Amer. Statist. 46 84-88.
[23] Smith, R. L. and Miller, J. E. (1986). A non-Gaussian state space model and application to prediction of records. J. R. Stat. Soc. Ser. B Stat. Methodol. 48 79-88. · Zbl 0593.62099
[24] Soyer, R. and Xu, F. (2010). Assessment of mortgage default risk via Bayesian reliability models. Appl. Stoch. Models Bus. Ind. 26 308-330. · Zbl 1226.91081
[25] Taufer, E. (2007). Modelling stylized features in default rates. Appl. Stoch. Models Bus. Ind. 23 73-82. · Zbl 1143.91023
[26] Uhlig, H. (1997). Bayesian vector autoregressions with stochastic volatility. Econometrica 65 59-73. · Zbl 0870.62092
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.