信用風險和資產(chǎn)證券化衍生品定價方法介紹_第一部分-信用風險理論介紹

1、金融工程案例分析課程， George Yuan， 2013-14第一部分第一部分: 信用風險理論介紹（信用風險理論介紹（2014年年7日上午日上午9:00am-11:30am）第1章信用風險介紹和信用評級第2章Merton 信用風險模型, KMV等模型應(yīng)用介紹第3章信用風險價值量調(diào)整(CVA)介紹第4章單因子結(jié)構(gòu)模型和信用風險價值量(Credit VaR) 介紹 第二部分第二部分: 信用和資產(chǎn)證券化衍生品定價信用和資產(chǎn)證券化衍生品定價( (2014年年7日下午日下午2:30pm-5:00pm) 第1章: 信用互換衍生品（CDS）定價介紹第2章: 資產(chǎn)證券化衍生品介紹第3章: 資產(chǎn)證券化衍生品定

2、價中南財大講學大綱中南財大講學大綱 信用風險和資產(chǎn)證券化衍生品定價方法介紹信用風險和資產(chǎn)證券化衍生品定價方法介紹袁先智（同濟大學風險管理研究所）第3頁2012-7-253一一信用風險管理的基本理論信用風險管理的基本理論目錄目錄金融工程案例分析課程， George Yuan， 2013-14第一部分第一部分: 信用風險理論介紹（信用風險理論介紹（2014年年7日上午日上午9:00am-11:30am）第第1章信用風險介紹和信用評級章信用風險介紹和信用評級第2章Merton 信用風險模型, KMV等模型應(yīng)用介紹第3章信用風險價值量調(diào)整(CVA)介紹第4章單因子結(jié)構(gòu)模型和信用風險價值量(Credit

3、 VaR) 介紹 中南財大講學大綱中南財大講學大綱 信用風險和資產(chǎn)證券化衍生品定價方法介紹信用風險和資產(chǎn)證券化衍生品定價方法介紹袁先智（同濟大學風險管理研究所）4第3頁2012-7-253一一Altman Score in Altman Score in 信用信用風險風險分析分析目錄目錄Altman Z-score IntroductionOriginal z-score component definitions variable definition weighting factorZ-score estimated for private firmsZ-score estimated f

4、or non-manufacturers & emerging markets金融工程案例分析課程， George Yuan， 2013-14目錄目錄- -Altman Score in Altman Score in 信用信用風險風險分析分析1. Altman Z-score Introduction1 Estimation of the formulaThe Z-score is a linear combination of four or five common business ratios, weighted by coefficients. The coefficients we

5、re estimated by identifying a set of firms which had declared bankruptcy and then collecting a matched sample of firms which had survived, with matching by industry and approximate size (assets).Altman applied the statistical method of discriminant analysis to a dataset of publicly held manufacturer

6、s. The estimation was originally based on data from publicly held manufacturers, but has since been re-estimated based on other datasets for private manufacturing, non-manufacturing and service companies.The original data sample consisted of 66 firms, half of which had filed for bankruptcy under Cha

7、pter 7. All businesses in the database were manufacturers, and small firms with assets of 2.99 -“Safe” Zones1.81 Z 2.99 -“Grey” ZonesZ 2.9 -“Safe” Zone1.23 Z 2.9 -“Grey” ZoneZ 3.75 -“Safe” Zone1.1 Z 3.75 -“Grey” ZoneZ化層化校正校正信用風險預(yù)期損失計量：客戶信用評級信用風險預(yù)期損失計量：客戶信用評級評級評級風險成本風險成本( (預(yù)期損失預(yù)期損失) )(EL

8、)(EL)=違約概率違約概率(PD)(PD)違約損失率違約損失率(LGD)(LGD)違約風險敞口違約風險敞口(EAD)(EAD)思想成就未來，專業(yè)創(chuàng)造價值第8頁50%50%75%75%100%100%有擔保有擔保清收清收損失損失無擔保收回無擔保收回比例比例擔保收回比擔保收回比例例債項評級對應(yīng)債項評級對應(yīng)LGDLGD0%0%25%25%信用風險預(yù)期損失計算：債項評級信用風險預(yù)期損失計算：債項評級客戶違約后不同業(yè)務(wù)的損失相同嗎？客戶違約后不同業(yè)務(wù)的損失相同嗎？風險暴露頭寸風險暴露頭寸無擔保無擔保風險成本風險成本( (預(yù)期損失預(yù)期損失) )(EL)(EL)=違約概率違約概率(PD)(PD)違約損失率

9、違約損失率(LGD)(LGD)違約風險敞口違約風險敞口(EAD)(EAD)違約損失率違約損失率(LGD)(LGD) 授信風險暴露授信風險暴露(EAD)(EAD)思想成就未來，專業(yè)創(chuàng)造價值第9頁信用風險預(yù)期損失計算示例信用風險預(yù)期損失計算示例舉例舉例1:1:評級為評級為A A的客戶、房產(chǎn)抵押的的客戶、房產(chǎn)抵押的1 1億元流動資金貸款，風險成本是多少？億元流動資金貸款，風險成本是多少？=客戶信用評級客戶信用評級0.30%0.30%違約概率違約概率(PD)(PD)債項評級債項評級貸款余額貸款余額50%50%1 1億元億元違約損失率違約損失率(LGD)(LGD) 授信風險暴露授信風險暴露(EAD)(E

10、AD)1515萬萬! !風險成本風險成本( (預(yù)期損失預(yù)期損失EL)EL)舉例舉例2:2:0.15%0.15%評級為評級為B B的客戶、房產(chǎn)抵押的的客戶、房產(chǎn)抵押的1 1億元流動資金貸款，風險成本是多少？億元流動資金貸款，風險成本是多少？=LGD)LGD) EAD)EAD)客戶信用評級客戶信用評級3.5%3.5%違約概率違約概率(PD)(PD)50%50%債項評級債項評級貸款余額貸款余額1 1億元億元175175萬萬! !風險成本風險成本( (預(yù)期損失預(yù)期損失EL)EL)1.75%!1.75%!第10頁信用風險的預(yù)期損失和非預(yù)期損失信用風險的預(yù)期損失和非預(yù)期損失預(yù)期損失預(yù)期損失nnnnn預(yù)期損

11、失(EL)是預(yù)計損失的平均值如果要獲得精確的預(yù)期損失，銀行必須對違約暴露、違約概率和違約損失率三項風險因素進行準確的計量可以被銀行所預(yù)見并成為需要考慮的經(jīng)營成本，實質(zhì)上并不構(gòu)成真正的風險在銀行提供的產(chǎn)品價格（如貸款利率）中得到了補償通過提取壞賬準備來抵補預(yù)期損失，影響銀行的當期損益非預(yù)期損失非預(yù)期損失nnnn非預(yù)期損失是損失圍繞預(yù)期損失的波動，它表現(xiàn)為風險損失標準差的若干倍違約事件可能存在相關(guān)性，當違約同時發(fā)生時，資產(chǎn)的價值將發(fā)生劇烈的變化非預(yù)期損失不能被預(yù)見，是真正意義上的風險，需要使用資本金來抵補非預(yù)期損失。通常，穩(wěn)健的銀行都應(yīng)至少保證資本金足以抵御概率99.9%以上的非預(yù)期損失非預(yù)期損失

12、也是PD、LGD和EAD的函數(shù)，只不過更加復(fù)雜信用風險非預(yù)期損失與經(jīng)濟資本信用風險非預(yù)期損失與經(jīng)濟資本概率經(jīng)濟資本量是在一定置信水平下（用評級表示）應(yīng)對非預(yù)期損失的能力。第11頁損失非預(yù)期損失是在一定置信水平上的風險損失衡量。置信水平越高，損失越大，但概率越低。經(jīng)濟資本不是真正的銀行資本，它是一個虛擬的資本數(shù)字，在數(shù)額上與非預(yù)期損失相等。某國際活躍銀行信用評級目標評級置信度A AA AAA99.9% 99.95% 99.99%第12頁信用風險的貸款定價信用風險的貸款定價貸款定價需要考慮的要素貸款定價需要考慮的要素目標利潤目標利潤總成本總成本根據(jù)盈利要求確定根據(jù)盈利要求確定考慮經(jīng)濟資本考慮經(jīng)濟資

13、本資金轉(zhuǎn)移價格資金轉(zhuǎn)移價格根據(jù)預(yù)期損失提根據(jù)預(yù)期損失提取減值準備取減值準備運營費用運營費用適用稅率適用稅率資本成本資本成本資金成本資金成本風險成本風險成本運營成本運營成本稅務(wù)成本稅務(wù)成本第3頁2012-7-253一一信用評級信用評級-Credit Ratings-Credit Ratings目錄目錄第13頁貸款收入貸款收入 - - 資金成本資金成本 - - 運營成本運營成本稅務(wù)成本稅務(wù)成本 - - 風險成本風險成本經(jīng)濟資本經(jīng)濟資本RAROCRAROC = =RAROCRAROC是考慮了風險的貸款盈利性指標，即是考慮了風險的貸款盈利性指標，即“風險調(diào)整后資本收益率風險調(diào)整后資本收益率”。風險調(diào)整

14、后資本收益率和經(jīng)濟增加值風險調(diào)整后資本收益率和經(jīng)濟增加值評價用評價用RAROCRAROC，兌現(xiàn)績效用，兌現(xiàn)績效用EVAEVA經(jīng)濟增加值經(jīng)濟增加值EVAEVA= = 貸款收入貸款收入 - - 資金成本資金成本 - - 運營成本運營成本 - - 稅務(wù)成本稅務(wù)成本 - - 風險成本風險成本資本成本資本成本即：即：EVAEVA = = 經(jīng)風險調(diào)整收益經(jīng)風險調(diào)整收益 資本成本資本成本第14頁信用風險限額管理信用風險限額管理復(fù)復(fù)雜雜程程度度風風險險反反映映程程度度基于風險等級限額基于風險等級限額基于經(jīng)濟資本的限額管理基于經(jīng)濟資本的限額管理低低高高高高基于貸款規(guī)?；谫J款規(guī)模經(jīng)濟資本配置管理是指以限額形式將

15、經(jīng)濟資本分解到各分支機構(gòu)、部門、產(chǎn)品、客戶等對象，并進行動態(tài)監(jiān)控和適時調(diào)整信用風險限額管理的發(fā)展：控制風險 風險收益的平衡第15頁信用風險集中度限額管理信用風險集中度限額管理信用集中度風險控制信用集中度風險限額管理信用集中度風險緩釋措施客戶集中度風險限額信用集中度風險組合限額監(jiān)管要求單一客戶單一集團客戶最大十家單一客戶行業(yè)維度資產(chǎn)組合再平衡地區(qū)維度產(chǎn)品維度機構(gòu)維度信貸資產(chǎn)組合管理信貸資產(chǎn)組合管理n銀行要管理單筆信貸資產(chǎn)風險，更要管理信貸資產(chǎn)組合風險。貸款組合風險絕不是單筆貸款風險銀行要管理單筆信貸資產(chǎn)風險，更要管理信貸資產(chǎn)組合風險。貸款組合風險絕不是單筆貸款風險的算術(shù)加總，需要考慮單筆貸款之間

16、的相關(guān)性。的算術(shù)加總，需要考慮單筆貸款之間的相關(guān)性。 資產(chǎn)組合管理的核心是掌握不同資產(chǎn)之間的風險資產(chǎn)組合管理的核心是掌握不同資產(chǎn)之間的風險相關(guān)性（疊加、消減和對沖等），從而利用資產(chǎn)相關(guān)性實現(xiàn)風險的對沖和消減，通過風險相關(guān)性配相關(guān)性（疊加、消減和對沖等），從而利用資產(chǎn)相關(guān)性實現(xiàn)風險的對沖和消減，通過風險相關(guān)性配置實現(xiàn)風險的對沖和消減，降低資產(chǎn)同時損失的可能性。置實現(xiàn)風險的對沖和消減，降低資產(chǎn)同時損失的可能性。n銀行整個資產(chǎn)組合可以按照不同方式劃分成不同的細分組合，比如不同地區(qū)組合、不同客戶對象組銀行整個資產(chǎn)組合可以按照不同方式劃分成不同的細分組合，比如不同地區(qū)組合、不同客戶對象組合、不同行業(yè)組合

17、等，最低層次是單個客戶的信貸資產(chǎn)組合。不同層次組合之間不但有兩兩相關(guān)性，合、不同行業(yè)組合等，最低層次是單個客戶的信貸資產(chǎn)組合。不同層次組合之間不但有兩兩相關(guān)性，還有多重相關(guān)性；不但有一個層次上的相關(guān)，還有不同層次之間的相關(guān)性。因此，信貸資產(chǎn)組合的還有多重相關(guān)性；不但有一個層次上的相關(guān)，還有不同層次之間的相關(guān)性。因此，信貸資產(chǎn)組合的研研究是一個龐大的體系。究是一個龐大的體系。第16頁+1+1-1-10 0相關(guān)系數(shù)相關(guān)系數(shù)風險消減效應(yīng)風險消減效應(yīng)最小最小最大最大第17頁銀監(jiān)會對公司客戶內(nèi)部評級體系的要求銀監(jiān)會對公司客戶內(nèi)部評級體系的要求總體要求評級維度評級結(jié)構(gòu)債務(wù)人評級方法論和評級時間跨度評級標準

18、nnn至少包括債務(wù)人評級和債項評級兩個維度債務(wù)人不同債項的債務(wù)人評級一致初級法、高級法對債項評級要求不同nn使用IRB確定非零售債務(wù)人、債項評級，債務(wù)人包括所有債務(wù)人與保證人計量模型法、專家判斷法或綜合應(yīng)用nnn債務(wù)人評級至少7個非違約級別，1個違約級別有效區(qū)分風險，較高級別的風險小于較低級別的風險風險在不同級別合理分布nnnnnnnn可以采取時點評級法、跨周期評級法以及介于兩者之間評級方法估計債務(wù)人的PD同時考慮影響債務(wù)人違約風險的非系統(tǒng)性和系統(tǒng)性因素應(yīng)估計債務(wù)人未來一年違約概率。監(jiān)管部門鼓勵商業(yè)銀行采用長于一年的時間跨度。模型使用計量模型應(yīng)在評估違約特征和損失特征中發(fā)揮重要作用。應(yīng)通過必要

19、的專家判斷保證內(nèi)部評級考慮了所有相關(guān)信息。可以根據(jù)業(yè)務(wù)的復(fù)雜程度以及風險管理水平建立多種評級體系監(jiān)測模型的預(yù)測能力，驗證模型，持續(xù)改進模型表現(xiàn)。對模型數(shù)據(jù)和假設(shè)的要求。nnnnn評級定義和標準應(yīng)合理、直觀，且能夠有意義地區(qū)分風險考慮與債務(wù)人和債項評級相關(guān)的所有重要信息。銀行擁有的信息越少，評級應(yīng)越保守。內(nèi)部評級可參考外部評級結(jié)果，但應(yīng)考慮其他信息。文檔化管理書面記錄非零售風險暴露內(nèi)部評級的設(shè)計。書面記錄內(nèi)部評級的重要過程、評級標準及各級別定義就模型的方法論、使用范圍等建立完整文檔技術(shù)要求第18頁內(nèi)部評級和五級分類內(nèi)部評級和五級分類nnnn內(nèi)部評級法是以歷史數(shù)據(jù)為基礎(chǔ)，通過數(shù)理統(tǒng)計分析方法，計算

20、借款人和債項的數(shù)據(jù)指標，并籍此開展信用風險管理。而五級分類則以主觀判斷為特征，缺乏必要的定量分析，而且沒有反映出貸款的實際損失。內(nèi)部評級法體現(xiàn)了對貸款發(fā)放的事先管理，強調(diào)通過分析既有的數(shù)據(jù)來預(yù)測和防范未來的風險，因而能有效地決定貸款發(fā)放與否、貸款發(fā)放額度、貸款利息水平以及抵押擔保的要求等。而五級分類則只能在事后的檢查或補救中發(fā)揮作用。內(nèi)部評級是二維評級系統(tǒng)。一維是針對借款人；另一維是針對債項的評級。五級分類則是一維評級系統(tǒng)，不區(qū)分借款人與債項這兩類不同性質(zhì)的風險以及影響這兩類風險的重要因素，因此，它并不能準確地反映風險，更不利于有效地防范風險。借助內(nèi)部評級，可以把五級分類細化為十二級分類。第1

21、9頁信用風險內(nèi)部評級法的風險暴露分類信用風險內(nèi)部評級法的風險暴露分類銀行賬戶的風險暴露分類金融機構(gòu)銀行類機構(gòu)風險暴露非銀行類機構(gòu)風險暴露兩類公司一般公司風險暴露專業(yè)貸款項目融資物品融資商品融資產(chǎn)生收入的房地產(chǎn)中小企業(yè)風險暴露零售個人住房抵押貸款風險暴露合格循環(huán)零售貸款風險暴露其它零售風險暴露股權(quán)銀行直接或間接持有的股東權(quán)益主權(quán)主權(quán)國家或經(jīng)濟實體區(qū)域及其中央銀行非中央政府公共部門實體適用零風險權(quán)重的多邊開發(fā)銀行、國際清算銀行、國際貨幣基金組織等的債權(quán)第20頁nnn信用風險管理應(yīng)與業(yè)務(wù)發(fā)展相協(xié)調(diào)，并滿足監(jiān)管要求。信用風險管理工具應(yīng)支持信貸業(yè)務(wù)人員，而不是取代或影響他們的權(quán)威。信用風險管理工具只有在

22、被理解的情況下，才能充分發(fā)揮作用。信用風險管理的基本理念信用風險管理的基本理念信用風險管理是銀行的核心能力信用風險管理是銀行的核心能力nn雖然定量工具對于信用風險管理的科學性具有重要作用，但是信用風險管理不是一門工程學科。對于歷史數(shù)據(jù)的分析相當有用，但其在信用風險管理中并不起決定性作用。業(yè)務(wù)專家的主觀判斷對于信用風險管理非常重要。n西方國家的模型開發(fā)技術(shù)，需要根據(jù)國內(nèi)中小銀行的數(shù)據(jù)質(zhì)量狀況和市場背景，有選擇地采用。信用風險管理是一門實用藝術(shù)信用風險管理是一門實用藝術(shù)nn為了達到風險管理的最佳效果，需要風險管理體系的各方面協(xié)調(diào)統(tǒng)一，包括：治理架構(gòu)、政策制度、工具方法、人員培訓(xùn)和信息科技等。只有在

23、一個完善的風險管理體系中，復(fù)雜的信用風險管理工具和方法，才能充分發(fā)揮其作用。風險管理是一個復(fù)雜的體系風險管理是一個復(fù)雜的體系金融工程案例分析課程， George Yuan， 2013-14Historical Data Historical data provided by rating agencies are also used to estimate the probability of default金融工程案例分析課程， George Yuan， 2013-14Cumulative Ave Default Rates (%) (1970-2009, Moodys, Table 23.

24、1, page 522) 1 2 3 4 5 7 10 Aaa 0.000 0.012 0.012 0.037 0.105 0.245 0.497 Aa 0.022 0.059 0.091 0.159 0.234 0.384 0.542 A 0.051 0.165 0.341 0.520 0.717 1.179 2.046 Baa 0.176 0.494 0.912 1.404 1.926 2.996 4.851 Ba 1.166 3.186 5.583 8.123 10.397 14.318 19.964 B 4.546 10.426 16.188 21.256 25.895 34.473

25、44.377 Caa-C 17.723 29.384 38.682 46.094 52.286 59.771 71.376 金融工程案例分析課程， George Yuan， 2013-14Interpretation The table shows the probability of default for companies starting with a particular credit rating A company with an initial credit rating of Baa has a probability of 0.176% of defaulting by t

26、he end of the first year, 0.494% by the end of the second year, and so on金融工程案例分析課程， George Yuan， 2013-14Do Default Probabilities Increase with Time? For a company that starts with a good credit rating default probabilities tend to increase with time For a company that starts with a poor credit rati

27、ng default probabilities tend to decrease with time 金融工程案例分析課程， George Yuan， 2013-14Hazard Rates vs Unconditional Default Probabilities (page 522-523) The hazard rate (also called default intensity) is the probability of default for a certain time period conditional on no earlier default The uncondi

28、tional default probability is the probability of default for a certain time period as seen at time zero What are the default intensities and unconditional default probabilities for a Caa rated company in the third year?金融工程案例分析課程， George Yuan， 2013-14Hazard Rate The hazard rate that is usually quote

29、d is an instantaneous rate If V(t) is the probability of a company surviving to time tttdttetQtetVtVttVttVt)()(1)()()()()()(0is timeby default ofy probabilit cumulative Theto leads This金融工程案例分析課程， George Yuan， 2013-1437Recovery Rate The recovery rate for a bond is usually defined as the price of the

30、 bond immediately after default as a percent of its face value Recovery rates tend to decrease as default rates increase金融工程案例分析課程， George Yuan， 2013-14Recovery Rates; Moodys: 1982 to 2009Class Mean(%) 1st lien bank loan 65.6 2nd lien bank loan 32.8 Sen Unsec. bank loan 48.7 Senior Secured 49.8 Seni

31、or Unsecured 36.6 Senior Subordinated 30.7 Subordinated 31.3 Junior Subordinated 24.7 金融工程案例分析課程， George Yuan， 2013-14Estimating Default Probabilities Alternatives:Use Bond PricesUse CDS spreadsUse Historical DataUse Mertons Model金融工程案例分析課程， George Yuan， 2013-14Using Bond Prices (Equation 23.2, page

32、 524)Average default intensity over life of bond is approximatelywhere s is the spread of the bonds yield over the risk-free rate and R is the recovery rateRs1金融工程案例分析課程， George Yuan， 2013-14More Exact Calculation Assume that a five year corporate bond pays a coupon of 6% per annum (semiannually). T

33、he yield is 7% with continuous compounding and the yield on a similar risk-free bond is 5% (with continuous compounding) Price of risk-free bond is 104.09; price of corporate bond is 95.34; expected loss from defaults is 8.75 Suppose that the probability of default is Q per year and that defaults al

34、ways happen half way through a year (immediately before a coupon payment. 金融工程案例分析課程， George Yuan， 2013-14Calculations (Table 23.3, page 525)金融工程案例分析課程， George Yuan， 2013-14Calculations continued We set 288.48Q = 8.75 to get Q = 3.03% This analysis can be extended to allow defaults to take place mor

35、e frequently With several bonds we can use more parameters to describe the default probability distribution金融工程案例分析課程， George Yuan， 2013-14The Risk-Free Rate The risk-free rate when default probabilities are estimated is usually assumed to be the LIBOR/swap zero rate (or sometimes 10 bps below the L

36、IBOR/swap rate) Asset swaps provide a direct estimates of the spread of bond yields over swap rates金融工程案例分析課程， George Yuan， 2013-14Real World vs Risk-Neutral Default Probabilities The default probabilities backed out of bond prices or credit default swap spreads are risk-neutral default probabilitie

37、s The default probabilities backed out of historical data are real-world default probabilities金融工程案例分析課程， George Yuan， 2013-14A Comparison Calculate 7-year default intensities from the Moodys data, 1970-2009, (These are real world default probabilities) Use Merrill Lynch data to estimate average 7-y

38、ear default intensities from bond prices, 1996 to 2007 (these are risk-neutral default intensities) Assume a risk-free rate equal to the 7-year swap rate minus 10 basis points金融工程案例分析課程， George Yuan， 2013-14Data from Moodys and Merrill Lynch Cumulative 7-year default probability (Moodys: 1970-2009)

39、Average bond yield spread in bps* (Merrill Lynch: 1996 to June 2007) Aaa 0.245% 35.74 Aa 0.384% 43.67 A 1.179% 58.68 Baa 2.996% 127.53 Ba 14.318% 280.28 B 34.473% 481.04 Caa 59.771% 1103.70 *The benchmark risk-free rate for calculating spreads is assumed to be the swap rate minus 10 basis points. Bo

40、nds are corporate bonds with a life of approximately 7 years. 金融工程案例分析課程， George Yuan， 2013-1448Real World vs Risk Neutral Hazard Rates (Table 23.4, page 527) 1 Calculated asln(1-d)/7 where d is the Moodys 7 yr default rate. For example, in the case of Aaa companies, d=0.00245 and -ln(0.99755)/7=0.0

41、004 or 4bps. For investment grade companies the historical hazard rate is approximately d/7. 2 Calculated as s/(1-R) where s is the bond yield spread and R is the recovery rate (assumed to be 40%). 金融工程案例分析課程， George Yuan， 2013-1449Average Risk Premiums Earned By Bond Traders 1 Equals average spread

42、 of our benchmark risk-free rate over Treasuries.2 Equals historical hazard rate times (1-R) where R is the recovery rate. For example, in the case of Baa, 26bps is 0.6 times 43bps.金融工程案例分析課程， George Yuan， 2013-1450Possible Reasons for These Results (The third reason is the most important) Corporate

43、 bonds are relatively illiquid The subjective default probabilities of bond traders may be much higher than the estimates from Moodys historical data Bonds do not default independently of each other. This leads to systematic risk that cannot be diversified away. Bond returns are highly skewed with l

44、imited upside. The non-systematic risk is difficult to diversify away and may be priced by the market金融工程案例分析課程， George Yuan， 2013-14Which World Should We Use? We should use risk-neutral estimates for valuing credit derivatives and estimating the present value of the cost of default We should use re

45、al world estimates for calculating credit VaR and scenario analysis金融工程案例分析課程， George Yuan， 2013-14第一部分第一部分: 信用風險理論介紹（信用風險理論介紹（2014年年7日上午日上午9:00am-11:30am）第1章信用風險介紹和信用評級第第2 2章章Merton Merton 信用風險模型信用風險模型, KMV, KMV等模型應(yīng)用介紹等模型應(yīng)用介紹第3章信用風險價值量調(diào)整(CVA)介紹第4章單因子結(jié)構(gòu)模型和信用風險價值量(Credit VaR) 介紹 中南財大講學大綱中南財大講學大綱 信用風險

46、和資產(chǎn)證券化衍生品定價方法介紹信用風險和資產(chǎn)證券化衍生品定價方法介紹袁先智（同濟大學風險管理研究所）金融工程案例分析課程， George Yuan， 2013-14Using Equity Prices: Mertons Model (page 530-531) Mertons model regards the equity as an option on the assets of the firm In a simple situation the equity value ismax(VT D, 0)where VT is the value of the firm and D is

47、the debt repayment required金融工程案例分析課程， George Yuan， 2013-14Equity vs. Assets The Black-Scholes-Merton option pricing model enables the value of the firms equity today, E0, to be related to the value of its assets today, V0, and the volatility of its assets, sVEV N dDeN ddVDrTTddTrTVVV0012102212()()l

48、n()();wheresss金融工程案例分析課程， George Yuan， 2013-14Volatilities sssEVVEEVVN dV0010()This equation together with the option pricing relationship enables V0 and sV to be determined from E0 and sE金融工程案例分析課程， George Yuan， 2013-14Example A companys equity is $3 million and the volatility of the equity is 80%

49、The risk-free rate is 5%, the debt is $10 million and time to debt maturity is 1 year Solving the two equations yields V0=12.40 and sv=21.23% The probability of default is N(d2) or 12.7%金融工程案例分析課程， George Yuan， 2013-14The Implementation of Mertons Model Choose time horizon Calculate cumulative oblig

50、ations to time horizon. This is termed by KMV the “default point”. We denote it by D Use Mertons model to calculate a theoretical probability of default Use historical data or bond data to develop a one-to-one mapping of theoretical probability into either real-world or risk-neutral probability of d

51、efault.金融工程案例分析課程， George Yuan， 2013-14The Implementation of Mertons Model KMV 模型介紹模型介紹Asset (A(t) = Debt (D(t) + Equity (E(t)Three main approaches to modeling credit risk in the finance literatureStructural approach: Assumptions are made about the dynamics of a firms assets, its capital structure,

52、and its debt and share holders. A firm defaults if the assets are insufficient according to some measure. A liability is characterized as an option on the firms assets.Reduced form approach: No assumptions are made concerning why a default occurs. Rather, the dynamics of default are exogenously give

53、n by the default rate (or intensity). Prices of credit sensitive securities can be calculated as if they were default free using the risk free rate adjusted by the level of intensity. Incomplete information approach: Combines the structural and reduced form approaches.Structural approach: default in

54、 the classical Merton model (1974).1. We want to use the structural approach to incorporate bond default risk in bond valuationThe value of the firms assets are assumed to follow the process, where is the instantaneous expected rate of return on assets, and is the standard deviation of the return on

55、 assets.Let D(t,T) be the date t market value of debt with promised payment B at date t. The second line in (18.2) says that the payoff to the creditors equals the promised payment (B) minus the payoff on a European put option written on the firms assets with exercise price B.Market value of firm de

56、bt, D(t)Let P(t,T) represent the current date t price of a default-free, zero-coupon bond that pays $1 at date T, where the bond conforms with the Vasicek model in Ch. 9. Pennacchi asserts that using results for pricing options (Ch. 9.3) when interest rates are random (as in 9.58), we can write Mark

57、et value of firm equity, E(t)Shareholder equity is similar to a call option on the firms assets, since at maturity the payoff to equity holders is max A(t) B, 0. However, shareholder equity is different from a European option if the firm pay dividends to shareholders prior to maturity as reflected i

58、n the first term of the last line in (18.4) where denotes the dividend rate.Critique of the Merton modelThe Merton model assumption is that the firm has a single issue of zero-coupon debt. That is unrealistic. Modeling multiple issues with different maturities and seniorities complicates default. In

59、 response some models have suggested that default occurs when the firms assets hit a lower boundary. That boundary has a monotonic relation to the firms total outstanding debt. The first passage time is when the value of the firms assets crosses through the lower boundary. First passage model - - bo

60、nd indenture provisions often include safety covenants that give bond holders the right to reorganize the firm if the value falls below a given barrier.The first passage model defines the survival probability as p(t,T) that the distance to default does not reach zero at any date between t and T. The