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題名 在序列相關因子模型下探討動態模型化投資組合信用風險
Dynamic modeling portfolio credit risk under serially dependent factor model
作者 游智惇
Yu, Chih Tun
貢獻者 劉惠美
游智惇
Yu, Chih Tun
關鍵詞 序列相關因子模型
投資組合信用風險
貝氏分析
蒙地卡羅最大概似法
蒙地卡 羅期望最大法
Serially dependent factor model
Portfolio credit risk
Bayesian inference
Monte Carlo Expectation Maximization
Monte Carlo maximum likelihood
日期 2011
上傳時間 30-Oct-2012 11:20:43 (UTC+8)
摘要 獨立因子模型廣泛的應用在信用風險領域，此模型可用來估計經濟資本與投資組合的損失率分配。然而獨立因子模型假設因子獨立地服從同分配，因而可能會得到估計不精確的違約機率與資產相關係數。因此我們在本論文中提出序列相關因子模型來改進獨立因子模型的缺失，同時可以捕捉違約率的動態行為與授信戶間相關性。我們也分別從古典與貝氏的角度下估計序列相關因子模型。首先，我們在序列相關因子模型下利用貝氏的方法應用馬可夫鍊蒙地卡羅技巧估計違約機率與資產相關係數，使用標準普爾違約資料進行外樣本資料預測，能夠證明序列相關因子模型是比獨立因子模型合理。第二，蒙地卡羅期望最大法與蒙地卡羅最大概似法這兩種估計方法也使用在本篇論文。從模擬結果發現，若違約資料具有較大的序列相關與資產相關特性，蒙地卡羅最大概似法能夠配適的比蒙地卡羅期望最大法好。
The independent factor model has been widely used in the credit risk field, and has been applied in estimating the economic capital allocations and loss rate distribution on a credit portfolio. However, this model assumes independent and identically distributed common factor which may produce inaccurate estimates of default probabilities and asset correlation. In this thesis, we address a serially dependent factor model (SDFM) to improve this phenomenon. This model can capture both dynamic behavior of default risk and dependence among individual obligors. We also address the estimation of the SDFM from both frequentist and Bayesian point of view. Firstly, we consider the Bayesian approach by applying Markov chain Monte Carlo (MCMC) techniques in estimating default probability and asset correlation under SDFM. The out-of-sample forecasting for S&P default data provide strong evidence to support that the SDFM is more reliable than the independent factor model. Secondly, we use two frequentist estimation methods to estimate the default probability and asset correlation under SDFM. One is Monte Carlo Expectation Maximization (MCEM) estimation method along with a Gibbs sampler and an acceptance method and the other is Monte Carlo maximum likelihood (MCML) estimation method with importance sampling techniques.
參考文獻 Basel Committee on Banking Supervision. Basel II: international convergence of capital measurement and capital standards: A revised framework, Consultative Document, Bank for International Settlements, 2004.
     
     Basel Committee on Banking Supervision. Basel II: International convergence of capital measurement and capital standards: A revised framework-comprehensive version, Consultative Document, Bank for International Settlements, 2006.
     
     Bluhm, C., Overbeck, L., and Wagner, C., An Introduction to Credit Risk Modeling, Chapman & Hall, New York, 2002.
     
     Booth, J. G. and Hobert, J. P., Maximizing generalized linear mixed models likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society Series B, Vol.61, No.1, pp.265-285, 1999.
     
     Carter, C. K. and Kohn, R., On Gibbs sampling for state space models, Biometrika, Vol. 81. No.3, pp.541-553, 1994.
     
     Crouhy, M. G., Jarrow, R. A. and Turnbull, S. M., The subprime credit crisis of 2007, The Journal of Derivatives, Vol.16, No.1, pp.81-110, 2008.
     
     Czado, C. and Pflűger, C., Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio, Applied Stochastic Models in Business and Industry, Vol.24, No.3, pp.237-259, 2008.
     
     de Jong, P. and Shephard, N., The simulation smoother for time series models, Biometrika, Vol.82, No.2, pp.339-350, 1995.
     Dagpunar, J. S., Simulation and Monte Carlo - with Applications in Finance and MCMC, Wiley, New York, 2007.
     
     Dempster, A. P., Laird, N. M., and Rubin, D., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society B, Vol.39, pp.1-38, 1997.
     
     Dwyer, D. W., The distribution of defaults and Bayesian model validation, Journal of Risk Model Validation, Vol.1, No.1, pp.23-53, 2007.
     
     Durbin, J. and Koopman, S. J., Monte Carlo maximum likelihood estimation for non-Gaussian state space models, Biometrika, Vol.84, No.3, pp.669-684, 1997.
     
     Durbin, J. and Koopman, S. J., A simple and efficient simulation smoother for state-space time series models, Biometrika, Vol.89, No.3, pp.603-616, 2002.
     
     Ebnöther, S. and Vanini, P., Credit portfolios: What defines risk horizons and risk measurement?, Journal of Banking & Finance, Vol.31, No.12, pp.3663-3679, 2007.
     
     Fruhwirth-Schnatter, S., Data augmentation and dynamic linear models, Journal of Time Series Analysis, Vol.15, No.2, pp.183-202, 1994.
     
     Gelfand, A. E. and Smith, A. F. M, Sampling based approaches to calculate marginal densities, Journal of American Statistical Association, Vol.85, pp.398-409,1990.
     
     Gelfand, A., Model determination using sampling-based methods, in: W. Gilks, S. Richardson, and D. Spiegelhalter, (eds.), Markov Chain Monte Carlo in Practice, Chapman & Hall, London, pp.145-161, 1996.
     
     Geweke, J., Monte carlo simulation and numerical integration, in: H. M. Amman, D. A. Kendrick, and J. Rust, (eds.), Handbook of Computational Economics, North-Holland, Amsterdam, pp.731-800, 1996.
     
     Glasserman, P. and Li, J., Importance sampling for portfolio credit risk. Management Science, Vol.51, No.11, pp.1643-1656, 2005.
     
     Gordy, M. and Heitfield, E., Estimating default correlation from short panels of credit rating, Working Paper, Federal Reserve Board, 2002.
     
     Gordy, M. B., A risk-factor model foundation for ratings-based capital rules, Journal of Finanial Intermediation, Vol.12, No.3, pp.199-232, 2003.
     
     Gössl, M., Predictions based on certain uncertainties - a Bayesian credit portfolio approach, Disscuss Paper, HypoVereinsbank, 2005.
     
     Greenberg, E., Introduction to Bayesian Econometrics, Cambridge University Press, New York, 2007.
     
     Gupton, G., Finger, C. and Bhatia, M., CreditMetricsTM, technical document, CreditMetrics, 1997.
     
     Hanson, S. and Schuermann, T., Confidence intervals for probabilities of default, Journal of Banking & Finance, Vol.30, No.8, pp.2281-2301, 2006.
     
     Kiefer, N. M., The probability approach to default probabilities, Risk, Vol.20, No.7, pp.146-150, 2007.
     
     
     Kiefer, N. M., Default estimation for low--default portfolios, Journal of Empirical Finance, Vol.16, No.1, pp.164-173, 2009.
     
     Kiefer, N. M., Default estimation and expert information, Journal of Business and Economic Statistics, Vol.28, No.2, pp.320-328, 2010.
     
     Kiefer, N. M., Default estimation, correlated defaults, and expert information, Journal of Applied Econometrics, Vol.26, No.2, pp.173-192, 2011.
     
     Kitagawa, G, Monte Carlo filter and smoother for non-Gaussian nonlinear state space model, Journal of Computational and Graphical Statistics, Vol.5, pp.1-25, 1996.
     
     Kitagawa, G, A self-organizing state-space model, Journal of the American Statistical Association, Vol.93, pp.1203-1215, 1998.
     
     Koopman, S. J. and Lucas, A., A non-Gaussian panel time series model for estimating and decomposing default risk, Journal of Business & Economic Statistics, Vol.26, pp.510-525, 2008.
     
     McNeil, A. J. and Wendin, J. P., Bayesian inferences for generalized linear mixed models of portfolio credit risk, Journal of Empirical Finance, Vol.14, No.2, pp.131-149, 2007.
     
     Moody’s, Moody’s: Global default rate on the rise, Announcement.
     
     Rachev, S. T., Hsu, J. S. J., Bagasheva, B. S. and Fabozzi, F. J., Bayesian Methods in Finance, Wiley, New York, 2008.
     
     
     Robert, C. and Casella, G., Monte Carlo Statistical Models, Springer, New York, 2004.
     
     Rösch, D, An empirical comparison of default risk forecasts from alternative credit rating philosophies, International Journal of Forecasting, Vol.21, pp.37-51, 2005.
     
     Schönbucher, P., Factor models: Portfolio credit risks when defaults are correlated, Journal of Risk Finance, Vol.3, No.1, pp.45-56, 2001.
     
     Shephard, N., Partial non-Gaussian state space, Biometrika, Vol.81, pp.115-132, 1994.
     
     Shephard, N. and Pitt, M. K., Likelihood analysis of non-Gaussian measurement time series, Biometrika, Vol.84, pp.653-667, 1997.
     
     Song, P. X.-K., Correlated Data Analysis: Modeling, Analytics, and Applications, Springer, New York, 2007.
     
     Soros, G., The New Paradigm for Financial Markets: The Credit Crisis of 2008 and What it Means, PublicAffairs, New York, 2008.
     
     Standard & Poor`s, Default, Transition, and Recovery: 2009 Annual Global Corporate Default Study and Rating Transitions, Technical Report, Global Fixed Income Research, 2009.
     
     Vasicek, O., Loan portfolio value, Risk, Vol.15, No.12, pp.160-162, 2002.
     
     Wei, G. C. G. and Tanner, M. A., A Monte Carlo implementation of the EM algorithm and the poor man`s data augmentation algorithms, Journal of American Statistical Association, Vol.85, pp.699-704, 1990.
     
     Wu, L., Non-linear mixed-effect models with non-ignorably missing covariates, The Canadian Journal of Statistics, Vol.32, No.1, pp.27-37, 2004.
描述 博士
國立政治大學
統計研究所
95354501
100
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0095354501
資料類型 thesis
dc.contributor.advisor 劉惠美zh_TW
dc.contributor.author (Authors) 游智惇zh_TW
dc.contributor.author (Authors) Yu, Chih Tunen_US
dc.creator (作者) 游智惇zh_TW
dc.creator (作者) Yu, Chih Tunen_US
dc.date (日期) 2011en_US
dc.date.accessioned 30-Oct-2012 11:20:43 (UTC+8)-
dc.date.available 30-Oct-2012 11:20:43 (UTC+8)-
dc.date.issued (上傳時間) 30-Oct-2012 11:20:43 (UTC+8)-
dc.identifier (Other Identifiers) G0095354501en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/54549-
dc.description (描述) 博士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計研究所zh_TW
dc.description (描述) 95354501zh_TW
dc.description (描述) 100zh_TW
dc.description.abstract (摘要) 獨立因子模型廣泛的應用在信用風險領域，此模型可用來估計經濟資本與投資組合的損失率分配。然而獨立因子模型假設因子獨立地服從同分配，因而可能會得到估計不精確的違約機率與資產相關係數。因此我們在本論文中提出序列相關因子模型來改進獨立因子模型的缺失，同時可以捕捉違約率的動態行為與授信戶間相關性。我們也分別從古典與貝氏的角度下估計序列相關因子模型。首先，我們在序列相關因子模型下利用貝氏的方法應用馬可夫鍊蒙地卡羅技巧估計違約機率與資產相關係數，使用標準普爾違約資料進行外樣本資料預測，能夠證明序列相關因子模型是比獨立因子模型合理。第二，蒙地卡羅期望最大法與蒙地卡羅最大概似法這兩種估計方法也使用在本篇論文。從模擬結果發現，若違約資料具有較大的序列相關與資產相關特性，蒙地卡羅最大概似法能夠配適的比蒙地卡羅期望最大法好。zh_TW
dc.description.abstract (摘要) The independent factor model has been widely used in the credit risk field, and has been applied in estimating the economic capital allocations and loss rate distribution on a credit portfolio. However, this model assumes independent and identically distributed common factor which may produce inaccurate estimates of default probabilities and asset correlation. In this thesis, we address a serially dependent factor model (SDFM) to improve this phenomenon. This model can capture both dynamic behavior of default risk and dependence among individual obligors. We also address the estimation of the SDFM from both frequentist and Bayesian point of view. Firstly, we consider the Bayesian approach by applying Markov chain Monte Carlo (MCMC) techniques in estimating default probability and asset correlation under SDFM. The out-of-sample forecasting for S&P default data provide strong evidence to support that the SDFM is more reliable than the independent factor model. Secondly, we use two frequentist estimation methods to estimate the default probability and asset correlation under SDFM. One is Monte Carlo Expectation Maximization (MCEM) estimation method along with a Gibbs sampler and an acceptance method and the other is Monte Carlo maximum likelihood (MCML) estimation method with importance sampling techniques.en_US
dc.description.tableofcontents 致謝辭 i
     中文摘要 ii
     Abstract iii
     Contents iv
     List of Tables vi
     List of Figures viii
     
     Chapter 1 Introduction 1
     1.1 Estimation of serially dependent factor model 2
     1.1.1 Bayesian point of view 3
     1.1.2 Frequentist point of view 3
     1.2 Outline of the thesis 5
     
     Chapter 2 Bayesian inferences for serially dependent factor model 6
     2.1 The serially dependent factor model 6
     2.2 Bayesian estimation and MCMC 8
     2.3 An empirical study of S&P default data 10
     2.3.1 The Choice of Prior Distribution 11
     2.3.2 Empirical Results 13
     2.3.3 Out-of-Sample Forecasts 21
     2.3.4 Quantify capital cushion 22
     2.4 Conclusions 27
     
     Chapter 3 MCEM estimation method for serially dependent factor model 28
     3.1 A Monte Carlo Expectation Maximization Method 28
     3.1.1 Estimation of 29
     3.1.2 Estimation of and 31
     3.2 An empirical study of the S&P default data 32
     3.3 Conclusions 35
     
     Chapter 4 MCML estimation method for serially dependent factor model 36
     4.1 A Monte Carlo Maximum likelihood Method 36
     4.1.1 Motivation 37
     4.1.2 Importance sampling Estimation 39
     4.2 An empirical study of the S&P default data 43
     4.3 Simulation results 47
     4.4 Conclusions 58
     Chapter 5 Conclusions 59
     
     Appendix A Acceptance method 60
     Appendix B Generalized linear mixed models 61
     Appendix C Economic capital 63
     Appendix D Kalman filter, disturbance smoother, state smoother algorithm, and state simulation algorithm. 65
     
     References 67		zh_TW
dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0095354501en_US
dc.subject (關鍵詞) 序列相關因子模型zh_TW
dc.subject (關鍵詞) 投資組合信用風險zh_TW
dc.subject (關鍵詞) 貝氏分析zh_TW
dc.subject (關鍵詞) 蒙地卡羅最大概似法zh_TW
dc.subject (關鍵詞) 蒙地卡 羅期望最大法zh_TW
dc.subject (關鍵詞) Serially dependent factor modelen_US
dc.subject (關鍵詞) Portfolio credit risken_US
dc.subject (關鍵詞) Bayesian inferenceen_US
dc.subject (關鍵詞) Monte Carlo Expectation Maximizationen_US
dc.subject (關鍵詞) Monte Carlo maximum likelihooden_US
dc.title (題名) 在序列相關因子模型下探討動態模型化投資組合信用風險zh_TW
dc.title (題名) Dynamic modeling portfolio credit risk under serially dependent factor modelen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) Basel Committee on Banking Supervision. Basel II: international convergence of capital measurement and capital standards: A revised framework, Consultative Document, Bank for International Settlements, 2004.
     
     Basel Committee on Banking Supervision. Basel II: International convergence of capital measurement and capital standards: A revised framework-comprehensive version, Consultative Document, Bank for International Settlements, 2006.
     
     Bluhm, C., Overbeck, L., and Wagner, C., An Introduction to Credit Risk Modeling, Chapman & Hall, New York, 2002.
     
     Booth, J. G. and Hobert, J. P., Maximizing generalized linear mixed models likelihoods with an automated Monte Carlo EM algorithm, Journal of the Royal Statistical Society Series B, Vol.61, No.1, pp.265-285, 1999.
     
     Carter, C. K. and Kohn, R., On Gibbs sampling for state space models, Biometrika, Vol. 81. No.3, pp.541-553, 1994.
     
     Crouhy, M. G., Jarrow, R. A. and Turnbull, S. M., The subprime credit crisis of 2007, The Journal of Derivatives, Vol.16, No.1, pp.81-110, 2008.
     
     Czado, C. and Pflűger, C., Modeling dependencies between rating categories and their effects on prediction in a credit risk portfolio, Applied Stochastic Models in Business and Industry, Vol.24, No.3, pp.237-259, 2008.
     
     de Jong, P. and Shephard, N., The simulation smoother for time series models, Biometrika, Vol.82, No.2, pp.339-350, 1995.
     Dagpunar, J. S., Simulation and Monte Carlo - with Applications in Finance and MCMC, Wiley, New York, 2007.
     
     Dempster, A. P., Laird, N. M., and Rubin, D., Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society B, Vol.39, pp.1-38, 1997.
     
     Dwyer, D. W., The distribution of defaults and Bayesian model validation, Journal of Risk Model Validation, Vol.1, No.1, pp.23-53, 2007.
     
     Durbin, J. and Koopman, S. J., Monte Carlo maximum likelihood estimation for non-Gaussian state space models, Biometrika, Vol.84, No.3, pp.669-684, 1997.
     
     Durbin, J. and Koopman, S. J., A simple and efficient simulation smoother for state-space time series models, Biometrika, Vol.89, No.3, pp.603-616, 2002.
     
     Ebnöther, S. and Vanini, P., Credit portfolios: What defines risk horizons and risk measurement?, Journal of Banking & Finance, Vol.31, No.12, pp.3663-3679, 2007.
     
     Fruhwirth-Schnatter, S., Data augmentation and dynamic linear models, Journal of Time Series Analysis, Vol.15, No.2, pp.183-202, 1994.
     
     Gelfand, A. E. and Smith, A. F. M, Sampling based approaches to calculate marginal densities, Journal of American Statistical Association, Vol.85, pp.398-409,1990.
     
     Gelfand, A., Model determination using sampling-based methods, in: W. Gilks, S. Richardson, and D. Spiegelhalter, (eds.), Markov Chain Monte Carlo in Practice, Chapman & Hall, London, pp.145-161, 1996.
     
     Geweke, J., Monte carlo simulation and numerical integration, in: H. M. Amman, D. A. Kendrick, and J. Rust, (eds.), Handbook of Computational Economics, North-Holland, Amsterdam, pp.731-800, 1996.
     
     Glasserman, P. and Li, J., Importance sampling for portfolio credit risk. Management Science, Vol.51, No.11, pp.1643-1656, 2005.
     
     Gordy, M. and Heitfield, E., Estimating default correlation from short panels of credit rating, Working Paper, Federal Reserve Board, 2002.
     
     Gordy, M. B., A risk-factor model foundation for ratings-based capital rules, Journal of Finanial Intermediation, Vol.12, No.3, pp.199-232, 2003.
     
     Gössl, M., Predictions based on certain uncertainties - a Bayesian credit portfolio approach, Disscuss Paper, HypoVereinsbank, 2005.
     
     Greenberg, E., Introduction to Bayesian Econometrics, Cambridge University Press, New York, 2007.
     
     Gupton, G., Finger, C. and Bhatia, M., CreditMetricsTM, technical document, CreditMetrics, 1997.
     
     Hanson, S. and Schuermann, T., Confidence intervals for probabilities of default, Journal of Banking & Finance, Vol.30, No.8, pp.2281-2301, 2006.
     
     Kiefer, N. M., The probability approach to default probabilities, Risk, Vol.20, No.7, pp.146-150, 2007.
     
     
     Kiefer, N. M., Default estimation for low--default portfolios, Journal of Empirical Finance, Vol.16, No.1, pp.164-173, 2009.
     
     Kiefer, N. M., Default estimation and expert information, Journal of Business and Economic Statistics, Vol.28, No.2, pp.320-328, 2010.
     
     Kiefer, N. M., Default estimation, correlated defaults, and expert information, Journal of Applied Econometrics, Vol.26, No.2, pp.173-192, 2011.
     
     Kitagawa, G, Monte Carlo filter and smoother for non-Gaussian nonlinear state space model, Journal of Computational and Graphical Statistics, Vol.5, pp.1-25, 1996.
     
     Kitagawa, G, A self-organizing state-space model, Journal of the American Statistical Association, Vol.93, pp.1203-1215, 1998.
     
     Koopman, S. J. and Lucas, A., A non-Gaussian panel time series model for estimating and decomposing default risk, Journal of Business & Economic Statistics, Vol.26, pp.510-525, 2008.
     
     McNeil, A. J. and Wendin, J. P., Bayesian inferences for generalized linear mixed models of portfolio credit risk, Journal of Empirical Finance, Vol.14, No.2, pp.131-149, 2007.
     
     Moody’s, Moody’s: Global default rate on the rise, Announcement.
     
     Rachev, S. T., Hsu, J. S. J., Bagasheva, B. S. and Fabozzi, F. J., Bayesian Methods in Finance, Wiley, New York, 2008.
     
     
     Robert, C. and Casella, G., Monte Carlo Statistical Models, Springer, New York, 2004.
     
     Rösch, D, An empirical comparison of default risk forecasts from alternative credit rating philosophies, International Journal of Forecasting, Vol.21, pp.37-51, 2005.
     
     Schönbucher, P., Factor models: Portfolio credit risks when defaults are correlated, Journal of Risk Finance, Vol.3, No.1, pp.45-56, 2001.
     
     Shephard, N., Partial non-Gaussian state space, Biometrika, Vol.81, pp.115-132, 1994.
     
     Shephard, N. and Pitt, M. K., Likelihood analysis of non-Gaussian measurement time series, Biometrika, Vol.84, pp.653-667, 1997.
     
     Song, P. X.-K., Correlated Data Analysis: Modeling, Analytics, and Applications, Springer, New York, 2007.
     
     Soros, G., The New Paradigm for Financial Markets: The Credit Crisis of 2008 and What it Means, PublicAffairs, New York, 2008.
     
     Standard & Poor`s, Default, Transition, and Recovery: 2009 Annual Global Corporate Default Study and Rating Transitions, Technical Report, Global Fixed Income Research, 2009.
     
     Vasicek, O., Loan portfolio value, Risk, Vol.15, No.12, pp.160-162, 2002.
     
     Wei, G. C. G. and Tanner, M. A., A Monte Carlo implementation of the EM algorithm and the poor man`s data augmentation algorithms, Journal of American Statistical Association, Vol.85, pp.699-704, 1990.
     
     Wu, L., Non-linear mixed-effect models with non-ignorably missing covariates, The Canadian Journal of Statistics, Vol.32, No.1, pp.27-37, 2004.		zh_TW