臺灣博碩士論文加值系統

「新巴賽爾資本協定」於2007年開始實施之後，已促使各銀行致力於提升風險管理能力，其中新巴賽爾資本協定第一支柱所規範的內部評等法，更成為眾多銀行努力追求的目標。然內部評等法用來計提資本的公式，卻是建立在許多簡化假設上，這些假設包括忽略違約機率及違約損失率之相關性、沒有集中度風險等等，且公式中所使用之參數亦直接引用國外資料。除了內部評等法，常見的商業化信用風險管理模型（如CreditMetrics、CreditRisk+等）亦均假設違約損失率為固定值，或假設為與違約機率獨立的隨機變數，無法處理違約機率及違約損失率相關議題。
有鑑於此，本文嘗試建立一個違約機率及違約損失率聯合模型，其中違約機率是由受總體因子影響的股票報酬率與受信用評等影響的報酬門檻所共同決定，而違約損失率則是由公司資產價值及預期負債所決定，其中資產價值由三種不同擔保力、折扣率資產所共同決定，預期負債比率則為總體因子決定。因此這個聯合模型的基本特色是違約機率及違約損失率將因同時受到總體因子影響而彼此相關。
將由台灣上市櫃公司實際資料所估計而得的參數值納入前述違約機率及違約損失率模型後，我們便可得到一個能夠進行蒙地卡羅模擬的完整架構，並得以此估算對應的經濟資本。模擬結果顯示，我們所估得的經濟資本要遠大於未考慮違約機率及損失率間相關性的經濟資本，也要比內部評等法所需計提之資本為大。此外為充分利用經濟資本作為風險定價的基礎乃至於考核風險調整後的績效，我們更進一步採用蒙地卡羅模擬方式將經濟資本配置至個別交易對手，這個模擬結果顯示個別交易對手相對風險的高低排序，與由內部評等法所得到的排序有相當大差異。
本文的主要結論是，銀行如欲精確衡量及妥善管理其信用風險，必須探究新巴賽爾資本協定所提供內部評等法資本計提公式的合理性，並依據其內部資料建構符合銀行特性的經濟資本模型，如此方有助於銀行有效的配置資本，也才更能符合新巴賽爾資本協定第二支柱的要求。若銀行能達此境界，則不僅銀行可賺得較大的風險調整後利益，其交易對手也可降低借貸成本，整體社會福利將因此獲得提升。

The implementation of Basel II in 2007 has driven banks to enhance their risk management capability, and the IRB approach has become the goal that many banks are aiming for. The IRB capital calculation formula is based on many assumptions including independence between PD and LGD, no concentration risk and identical parameters applying to all countries. Popular credit risk models like CreditMetrics or CreditRisk+ also make assumptions that LGDs are constant or LGDs are independent of PDs and do not explicitly deal with the dependence issue between PD and LGD.
For this reason, we try to build a joint model for PD and LGD. The PDs depend on expected stock returns, which are in turn affected by a common factor, as well as return thresholds that are determined by risk ratings. In contrast, LGDs depend on asset values and expected equity/debt ratios, in which asset values are decomposed to three categories with different guarantee powers, while expected equity/debt ratios are influenced by the common factor. The central idea of this joint model is that PD and LGD are both affected by the common factor and hence are correlated.
Viewing listed companies in Taiwan as a portfolio, we could estimate all parameters of our joint model and run Monte Carlo simulation to generate portfolio’s credit loss distribution and calculate the corresponding economic capital. The simulated economic capital is larger than the economic capital under the independence assumption and is also larger than the IRB capital. In addition, to employ economic capital as the basis for risk pricing and risk adjusted performance measurement, we must allocate portfolio economic capital to individual counterparty, which requires further Monte Carlo simulations. From the simulations, we find the ranking of allocated economic capital substantially differs from the ranking of IRB capital.
Our main conclusion is that banks need to explore the basic idea of IRB capital formula and use their internal data to construct economic capital models if they want to correctly measure and manage credit risks. Banks could then meet the requirement of the Pillar II in Basel II and allocate economic capital much more efficiently. Banks need to access loans according to comparative risk. Only when this is accomplished, will banks earn more risk adjusted profit. Their counterparty would also bear less financing cost. Social welfare could therefore improve.

第一章 前言 1

第二章 基礎信用損失模型 8
第1節 單一交易對手的違約機率 8
第2節 單一交易對手的違約損失率及違約曝險額 14
2.1 違約損失率的衡量方法 14
2.2 違約損失率基本特性 15
2.3 違約損失率的模型 16
第3節 信用損失分配的推導 18
3.1 簡化模型的信用損失分配 19
3.2 完整模型之信用損失分配—同質假設 22
3.3 完整模型之信用損失分配—異質假設 25
第4節 異質性及相關性對信用損失分配之影響 29

第三章 違約機率及損失率之結構式信用損失模型 31
第1節 結構式違約機率模型 31
第2節 結構式違約損失率模型 33
第3節 違約損失率期望值 40
第4節 預期損失與非預期損失 42
第5節 小結 47

第四章 組合資產信用損失模型實證結果 49
第1節 蒙地卡羅模擬基本設定 49
第2節 結構式違約損失率模型模擬 53
第3節 基礎信用損失模型模擬 58
第4節 違約機率及損失率之結構式信用損失模型模擬 61
第5節 小結 67

第五章 組合資產違約機率及違約損失率之相關性 69
第1節 違約機率及違約損失率之相關性 70
第2節 基本分析 74
第3節 加入違約損失率不得為負值之限制 80
第4節 考慮折扣率受共同因子影響 83
第5節 小結 88

第六章 經濟資本配置—兼與Basel II資本計提比較 90
第1節 經濟資本配置方法說明 90
第2節 用風險值及ES進行經濟資本配置 93
第3節 異質曝險下之經濟資本配置 98
第4節 應用風險抵減技術對經濟資本配置之影響 103
第5節 小結 106

第七章 結論 108

參考文獻 113

附錄1：IRB資本計提公式 117
附錄2：個別交易對手之損失期望值、變異數及交易對手間相關係數 118
附錄3：Hanson, Pesaran, and Schuermann (2007) 異質設定方式及僅假設無條件違約機率異質時預期損失之推導 119
附錄4：第三章部分數式之證明或推導 121
附錄5：檢視蒙地卡羅模擬做資本配置之合理性 124

Acharya, V. V., S. Bharath and A. Srinivasan (2008), “Does Industry-wide Distress Affect Defaulted Firms? – Evidence from Creditor Recoveries,” Journal of Financial Economics, forthcoming.
Altman, E. I., A. Resti, and A. Sironi (2001), Analyzing and Explaining Default Recovery Rates, ISDA research report, London.
Altman, E. I., B. Brady, A. Resti, and A. Sironi (2005), “The Link Between Default and Recovery Rates: Theory, Empirical Evidence and Implications,” Journal of Business, 78, 2203-2227.
Altman, E. I. (2006), “Default Recovery Rates and LGD in Credit Risk Modeling and Practice: An Updated Review of the Literature and Empirical Evidence,” Working Paper.
Basel Committee on Banking Supervision (2004a), “International Convergence of Capital Measurement and Capital Standards,” BIS.
Basel Committee on Banking Supervision (2004b), “Background Note on LGD Quantification,” BIS.
Basel Committee on Banking Supervision (2005a), “Studies on the Validation of Internal Rating System,” BIS.
Basel Committee on Banking Supervision (2005b), “Guidance on Paragraph 468 of the Framework Document,” BIS.
Basel Committee on Banking Supervision (2005c), “An Explanatory Note on the Basel II IRB Risk Weight Functions,” BIS.
Bluhm, C., L. Overbeck and C. Wagner (2003), An Introduction to Credit Risk Modeling, Boca Raton, FL: Chapman and Hall/CRC.
Carey, M. (1998), “Credit Risk in Private Debt Portfolios,” Journal of Finance, 53, 1363-1387.
Crosbie, P. and J. Bohn (2003), “Modeling Default Risk,” one report from Moody’s KMV, New York.
Dermine, J. and C. N. de Carvalho (2006), “Bank Loan Losses-Given-Default: A Case Study,” Journal of Banking and Finance, 30, 1219-1243.
de Servigny, A. and O. Renault (2003), “Correlation Evidence,” Risk, 16, 90-94.
de Servigny, A. and O. Renault (2004), Measuring and Managing Credit Risk, New York: McGraw-Hill.
Elizalde, A. (2005), “Credit Risk Models II: Structural Models,” Working Paper.
Frye, J. (2000a), “Collateral Damage,” Risk, 13, 91-94.
Frye, J. (2000b), “Depressing Recoveries,” Risk, 13, 108-111.
Gordy, M. B. (2000), “A Comparative Anatomy of Credit Risk Models,” Journal of Banking and Finance, 24, 119-149.
Gordy, M. B. and E. Heitfield (2002), “Estimating Default Correlation from Short Panels of Credit Rating Performance Data,” Working Paper, Federal Reserve Board.
Gordy, M. B. (2003), “A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules,” Journal of Financial Intermediation, 12, 199-232.
Gupton, G. M., C. C. Finger and M. Bhatia (1997), CreditMetricsTM — Technical Document, JPMorgan & Co., New York.
Gupton, G. M., D. Gates and L. V. Carty (2000), “Bank Loan Loss Given Default,” one report from Moody’s Investors Service.
Gupton, G. M. (2005), “Advancing Loss Given Default Prediction Models How the quiet have quickened,” Economic Notes, 34, 185-230.
Hanson, S. G., M. H. Pesaran and T. Schuermann (2007), “Firm Heterogeneity and Credit Risk Diversification,” forthcoming, Journal of Empirical Finance.
Hu, Y. T., and W. Perraudin (2002), “The Dependence of Recovery Rates and Defaults, ” Working Paper.
Hu, Y. T. (2005), “Extreme Correlation of Defaults and LGDs, ” Working Paper.
Jagannathan, R. and Z. Wang (1996), “The Conditional CAPM and the Cross-Section of Expected Returns, ” Journal of Finance, 51, 3-53.
Jokivuolle, E. and S. Peura (2000), “A Model for Estimating Recovery Rates and Collateral Haircuts for Bank Loans,” Working Paper.
Jokivuolle, E. and S. Peura (2003), “Incorporating Collateral Value Uncertainty in Loss Given Default Estimates and Loan-to-Value Ratios,” European Financial Management, 9, 299-314.
Lucas, D. (1995), “Default Correlation and Credit Analysis,” Journal of Fixed Income, 4, 76-87.
Lucas, A., P. Klaasen, P. Spreij and S. Straetmans (2001), “An Analytic Approach to Credit Risk of Large Corporate Bond and Loan Portfolios,” Journal of Banking and Finance, 25, 1635-1664.
Maclachlan, I. (2004), “Choosing the Discount Factor for Estimating Economic LGD,” Working Paper.
Merton, R. C. (1974), “On the Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, 29, 449-470.
Miu, P. and B. Ozdemir (2006), “Basel Requirement of Downturn LGD: Mmodeling and Estimating PD and LGD Correlations,” The Journal of Credit Risk, 2, 43-68.
Pesaran, M. H., T. Schuermann, B. Treutler, and S. M. Weiner (2006), “Macroeconomic Dynamics and Credit Risk: A Global Perspective,” Journal of Money, Credit and Banking, 38, 1211-1261.
Renault, O. and O. Scaillet (2004), “On the Way to Recovery: A Nonparametric Bias Free Estimation of Recovery Rate Densities,” Journal of Banking and Finance, 24, 2915-2931.
Schuermann, T. (2006), “What do We Know About Loss Given Default,” in Altman et al. (ed.), Recovery Risk, 3-24, London, UK, Risk Books.
Tasche, D. (2000), “Conditional Expectation as Quantile Derivative,” Working Paper, Munich University of Technology.
Vasicek, O. (1987), “Probability of Loss on Loan Portfolio,” one report from Moody’s KMV, New York.
Vasicek, O. (1991), “Limiting Loan Loss Distribution,” one report from Moody’s KMV, New York.
Wei, S. (2006), “Credit Risk: Modeling and Application,” Working Paper.
Wilson, T. (1997a), “Portfolio Credit Risk, Part I,” Risk, 10, 111-117.
Wilson, T. (1997b), “Portfolio Credit Risk, Part II,” Risk, 10, 56-61.