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| Title: | 多期數之信用風險違約機率驗證法
The Calibration Method of Probability of Default under Multiple Periods |
| Authors: | 林福文
Lin, Fu-Wen |
| Contributors: | 劉惠美
陳麗霞
Liu, Huimei
Chen, Li-Shya
林福文
Lin, Fu-Wen |
| Keywords: | 紅綠燈檢定
卜瓦松映射
二項映射
Traffic lights test
Poisson mapping
Binomial mapping with granularity adjustment |
| Date: | 2009 |
| Issue Date: | 2013-09-05 15:10:09 (UTC+8) |
| Abstract: | 新巴賽爾資協定中，針對銀行風險管理具備三大支柱，支柱一管理信用風險、市場風險及作業風險，其中信用風險方法更分為標準法、基礎內部模型法與進階內部模型法。不論銀行採用何種內部模型法，銀行必須有估計違約機率之能力，並且送交監理機關審查核准。為了確保預測違約機率之適當，巴賽爾銀行監理委員會BCBS (2005) 對於不同資料長度與驗證期間分別建議二項檢定、卡方檢定、常態檢定與紅綠燈檢定。當資料期數足夠時，BCBS推薦使用紅綠燈檢定，但該檢定需要若干假設：違約事件間相互獨立且違約事件在時間上亦獨立，因此在BCBS (2005) 中之某些情境下，採用紅綠燈檢定驗證違約機率會受到違約事件之間並非獨立，造成中央極限定理不適當地近似標準化之違約機率至常態分配，且模擬之型一誤差亦有高估之結果。
在違約事件之間獨立且無時間相關性下，本文建議採用卜瓦松分配近似二項分配；在違約事件之間非獨立且具有時間相關性下，本文則建議採用二項分配，結合granularity adjustment，使違約事件間之相關性可以反映在不同顏色之分色點上。最後，由數量模擬結果顯示：本文建議採用之改良方法，皆可有效將型一誤差維持在設定之顯著水準上，並反映真實之檢定力。因此，不論對銀行或監理機關來說，改良之違約機率驗證方法係值得使用之方法。
There are three methods in Basel II (Standardized Approach, Foundation IRB Approach and Advanced IRB Approach) to calculate the capital charges. The banks have to estimate probability of default (PD) if they use IRB approach. Four statistic methods recommended by BCBS worthy to validate the PD: Binomial test, Chi-square test, Normal test and Extended Traffic Lights test (ETLT). If the data are long enough, BCBS recommended using the ETLT with the assumptions that the obligors are independent and also independent in time. From numerical results, validating PDs by ETLT will overestimate the type I errors and statistic power.
We suggest two methods in different scenarios to make the type I errors closed to the significant level. First, we suggest to approximate Normal distribution in Poisson distribution with randomization technique. Second, we combine Binomial distribution with granularity adjustment to fit the correlation between the obligors. Both methods not only perform well in type I errors, but also reflect the real statistic power. For the banks, both methods are worthy to use for avoiding to increasing the capital charges unexpectedly or the operational risk of the banks. |
| Reference: | 中文部分
張揖平，洪明欽，尹晟龢 (2009), “違約機率驗證之檢定”, 中國統計學報, Vol.47 113–128
英文部分
Basel Committee on Banking Supervision (BCBS) (2005), Studies on the Validation of Internal Rating Systems.
Blochwitz, S., Hohl, S., Tasche, D., and When, C. S. (2004), “Validating default probabilities on short time series”, Working paper.
Blochwitz, S., Hohl, S., and When, C. S. (2005), “Reconsidering ratings”, Wilmott magazine, May, 60–69.
Gordy, M. (2002), “A risk-factor model foundation for ratings-based bank capital rules”, Working paper.
Martin, R. and Wilde, T. (2002), “Unsystematic credit risk”, Risk magazine 15(11) 123–128.
Tasche D. (2003). “A traffic lights approach to PD validation”, Working paper. |
| Description: | 碩士
國立政治大學
統計研究所
97354006
98 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0097354006 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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| 400601.pdf | | 860Kb | Adobe PDF2 | 416 | View/Open |
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