《CreditRiskManagement》由会员分享，可在线阅读，更多相关《CreditRiskManagement（85页珍藏版）》请在金锄头文库上搜索。
1、Credit Risk Management1. Introduction to Credit Risk Management1.1 1.1 Definition and formsDefinition and forms1.2 Nature and Characteristics 1.2 Nature and Characteristics 1.3 Measurement1.3 Measurement1.4 Management Strategies, and Instruments 1.4 Management Strategies, and Instruments 1.5 History
2、 and Regulation1.5 History and Regulation1.6 Traditional CRM vs. Modern CRM1.6 Traditional CRM vs. Modern CRM1.1 Definition and formsn nBroadly defined, credit risk is the risk that a Broadly defined, credit risk is the risk that a counterparty will fail to perform an obligation to counterparty will
3、 fail to perform an obligation to the FI,or, a change in the credit quality of a the FI,or, a change in the credit quality of a counterparty will affect the value of an FIs counterparty will affect the value of an FIs position.position.n nDefault riskDefault riskn nCounterparty riskCounterparty risk
4、n nCredit migration riskCredit migration riskn nCredit event risk Credit event risk n nSettlement risk,(partly due to credit risk)Settlement risk,(partly due to credit risk)n nSovereign riskSovereign riskCredit risk facingn nLenders: default risk, loan revaluation riskLenders: default risk, loan rev
5、aluation riskn nBond holders: rating change(credit migration) Bond holders: rating change(credit migration) riskriskn nTraders of derivatives, equity and others: Traders of derivatives, equity and others: counterparty risk and settlement riskcounterparty risk and settlement riskWhat cause credit ris
6、k?n nFactors affecting the capability of borrowers: cash Factors affecting the capability of borrowers: cash flow from different sources: flow from different sources: n nFactors affecting the willingness of borrowersFactors affecting the willingness of borrowers Does credit risk refer to the type wh
7、ich borrowers Does credit risk refer to the type which borrowers refuse to repay money due to legal (contract) refuse to repay money due to legal (contract) reason, ownership reason, or fraud reason and reason, ownership reason, or fraud reason and other non-economic reason?other non-economic reason
8、?n nInformation asymmetry and incentive (agency) Information asymmetry and incentive (agency) problem will worsen the situationproblem will worsen the situation a: agency problem between lender and borrower a: agency problem between lender and borrower b: agency problem between management and b: age
9、ncy problem between management and shareholdershareholder1.2 Nature and Characteristicsn nCounterparty risk, firm-specific (unsystematic) risk Counterparty risk, firm-specific (unsystematic) risk Diversification and avoiding concentration is important principle Diversification and avoiding concentra
10、tion is important principle of credit risk management.of credit risk management.n nInformation Asymmetry and Moral hazard Information Asymmetry and Moral hazard People-and-system-focused internal control plays important People-and-system-focused internal control plays important role in credit risk m
11、anagement.role in credit risk management.n nAsymmetry nature and fat tail of frequency distribution (PDF)Asymmetry nature and fat tail of frequency distribution (PDF) Normality can no longer be an appropriate assumption in credit Normality can no longer be an appropriate assumption in credit risk me
12、asuring and loan pricing model. risk measuring and loan pricing model. n nIlliquidity and scarcity of data(except for tradable bond) Illiquidity and scarcity of data(except for tradable bond) Credit risk is more difficult to measure than market risk and Credit risk is more difficult to measure than
13、market risk and mark-to-market is hard to be applied to credit risk management. mark-to-market is hard to be applied to credit risk management. Mark-to-model is taken instead. Mark-to-model is taken instead. PDF of Loss (Actual vs Normal) Frequency(Loan loss)(Loan value)0FrequencyNo defaultMaximum L
14、oss0Maximum valueFat tailExpected lossExpected valueNormal, bell-shaped distributionActual distribution1.3 Measurementn nTraditional approachesTraditional approaches Expert system, rating system, scoring system Expert system, rating system, scoring systemn nModern approachesModern approaches Credit
15、spread derivation model, Credit spread derivation model, Mortality rate derivation model, Mortality rate derivation model, RAROC model, RAROC model, Creditmetics model Creditmetics model KMV Portfolio Manager model KMV Portfolio Manager model CreditRisk+ model CreditRisk+ modelTasks of credit risk m
16、easurementn nProbability of DefaultProbability of Defaultn nLoss Given Default (=1-recovery rate)Loss Given Default (=1-recovery rate)n nExpected lossExpected lossn nUnexpected LossUnexpected Lossn nExpected lossExpected loss =Loan sizeProbability of DefaultLoss Given Default =Loan sizeProbability o
17、f DefaultLoss Given Default =Expected value of loss distribution =Expected value of loss distributionn nReserve should be held for expected loss, and pricing should Reserve should be held for expected loss, and pricing should include this elementinclude this elementn nUnexpected Loss=a particular va
18、lue of loss distribution at a Unexpected Loss=a particular value of loss distribution at a prespecified confidence level, or a worst-scenario lossprespecified confidence level, or a worst-scenario lossn nCapital should be held for unexpected loss, and pricing should Capital should be held for unexpe
19、cted loss, and pricing should include ROEinclude ROELoss distribution, Loss reserve, and Capital requirement Magnitude of loss0Frequency Expected lossUnexpected Loss prespecified confidence level, e.g.99%Fat tailMinimum lossNo defaultMaximum1.4 Management Strategies, and Instrumentsn nTraditional: T
20、raditional: 1. Risk retain and pricing (self-insurance) 1. Risk retain and pricing (self-insurance) 2. Risk retain and internal control 2. Risk retain and internal control 3. Risk transferring through risk mitigation 3. Risk transferring through risk mitigation covenantscovenants 4. Risk reducing th
21、rough restrictive covenants 4. Risk reducing through restrictive covenants 5. Diversification 5. Diversificationn nModern:Modern: 1. Market hedging and credit derivatives 1. Market hedging and credit derivatives 2. Securitization and loan sale 2. Securitization and loan sale 1.5 History and Regulati
22、onn nTraditional banking risk and traditional Traditional banking risk and traditional management methodsmanagement methodsn nBasel Capital Accord 1988Basel Capital Accord 1988n nEvolvement to modern credit managementEvolvement to modern credit managementn nBasel Capital Accord 2000+Basel Capital Ac
23、cord 2000+n nFrom default risk in banking book to counterparty From default risk in banking book to counterparty risk in trading bookrisk in trading bookn nRegulatory response to credit derivatives Regulatory response to credit derivatives 1.6 Traditional CRM vs. Modern CRM Traditional CRM Tradition
24、al CRMn nLong historyLong historyn nIndividual approachIndividual approachn nExpert systemExpert systemn nBook value approachBook value approachn nMark to bookMark to bookn nNo hedging No hedging n nRemained on bookRemained on book Modern CRM Modern CRMn nRecent yearsRecent yearsn nPortfolio approac
25、hPortfolio approachn nScientific modelsScientific modelsn nMarket value approachMarket value approachn nMark to market or Mark to market or modelmodeln nCredit derivativeCredit derivativen nIntegrated with Integrated with market market 2. Credit analysis and credit risk measuring: Traditional approa
26、ch2.1 Expert system 2.1 Expert system 2.2 Rating system 2.2 Rating system 2.3 Credit scoring system2.3 Credit scoring system2.1 Expert systemn nThree elements of credit decision and risk Three elements of credit decision and risk managementmanagementn nCharacteristics of expert systemCharacteristics
27、 of expert systemn n5Cs 5Cs n nProcess of credit analysis Process of credit analysis n nShifting emphasis form the balance sheet to cash Shifting emphasis form the balance sheet to cash flowflown nCommonly used financial ratios Commonly used financial ratios n nMajor problemsMajor problemsThree elem
28、ents of credit decision and risk managementn nPeoplePeoplen nProcess and SystemProcess and Systemn nAnalytic tools and technologyAnalytic tools and technology5Csn nCharacterCharactern nCapitalCapitaln nCapacityCapacityn nCollateralCollateraln nCycle or (Economic) ConditionsCycle or (Economic) Condit
29、ionsn n+ level of interest rates (nonlinear relationship + level of interest rates (nonlinear relationship between the level of interest rates and the between the level of interest rates and the expected return on a loan )expected return on a loan ) n nBorrower-specific factorsBorrower-specific fact
30、ors 1. Reputation (Character) 1. Reputation (Character) 2. Leverage (Capital) 2. Leverage (Capital) 3. Volatility of earnings (Capacity) 3. Volatility of earnings (Capacity) 4. Collateral 4. Collateral n nMarket-specific factors Market-specific factors 1. Business cycle, 1. Business cycle, 2. Intere
31、st rates 2. Interest ratesCharacteristics of expect systemn nSubjectiveSubjectiven nExperience of the senior lender is valuableExperience of the senior lender is valuablen nCredit culture plays important roleCredit culture plays important rolen nShift of emphasis from balance sheet to cash flowShift
32、 of emphasis from balance sheet to cash flown nDefault-focus Default-focus Commonly used financial ratiosn nSee Handouts Main problems of 5C expert systemn nSubjectivitySubjectivityn nConsistency and lack of common standards Consistency and lack of common standards among different credit officersamo
33、ng different credit officers Mechanism and effectiveness of loan committees Mechanism and effectiveness of loan committees or multiplayered signature authorities or multiplayered signature authorities n nHuman error, bureaucracy and operational riskHuman error, bureaucracy and operational risk2.3 Ra
34、ting system n n2.3.1 External rating2.3.1 External ratingn n2.3.2 Internal rating2.3.2 Internal rating2.3.1 External ratingn nWhat is credit rating?What is credit rating? n nMission of rating agenciesMission of rating agenciesn nFour major US rating agenciesFour major US rating agenciesn nRatings of
35、 Standard&Poor and MoodysRatings of Standard&Poor and Moodysn nClasses of credit ratingClasses of credit ratingn nPower of ratingPower of ratingn nIndependence of credit ratingIndependence of credit ratingn nMoodys Rating Analysis of an Industrial CompanyMoodys Rating Analysis of an Industrial Compa
36、nyn nS&Ps debt rating processS&Ps debt rating processn nRating focus of S&PRating focus of S&PWhat is credit rating?n nA credit rating is not, in general, an investment A credit rating is not, in general, an investment recommendation concerning a given recommendation concerning a given security(bond
37、).security(bond).n nS&P: “A credit rating is S&Ps opinion of the S&P: “A credit rating is S&Ps opinion of the general creditworthiness of an obligor, or the general creditworthiness of an obligor, or the creditworthiness of an obligor with respect to a creditworthiness of an obligor with respect to
38、a particular debt security or other financial particular debt security or other financial obligation, based on relevant risk factors.”obligation, based on relevant risk factors.”n nMoodys: a rating is “an opinion on the future Moodys: a rating is “an opinion on the future ability and legal obligatio
39、n of an issuer to make ability and legal obligation of an issuer to make timely payments of principal and interest on a timely payments of principal and interest on a specific fixed-income security”specific fixed-income security”Mission of rating agenciesn nAimed to serve and protect investors by Ai
40、med to serve and protect investors by providing independent and unbiased evaluation providing independent and unbiased evaluation on the creditworthiness of corporate, municipal, on the creditworthiness of corporate, municipal, and sovereign issues of debt securities.and sovereign issues of debt sec
41、urities.n nMore specifically, it is their job to inform investors More specifically, it is their job to inform investors about the likelihood that they will receive all about the likelihood that they will receive all principal and interest payments as scheduled for principal and interest payments as
42、 scheduled for a given security (Probability of default ); and if a given security (Probability of default ); and if default should occur, what level of recovery can default should occur, what level of recovery can be expected( Loss given Default)be expected( Loss given Default)n nRating agencies se
43、rves as watch dogs and early Rating agencies serves as watch dogs and early warning system of capital market.warning system of capital market.Four major US rating agenciesn nMoodys Investors ServiceMoodys Investors Servicen nStandard&Poors(S&P)Standard&Poors(S&P)n nFitch IBCAFitch IBCAn nDuff and Ph
44、elps Credit rating Co.Duff and Phelps Credit rating Co.Ratings of Standard&Poor and Moodys S&P MoodysS&P MoodysAAA AaaAAA AaaAA AaAA AaA AA ABBB BaaBBB BaaBB BaBB BaB BB BCCC CaaCCC CaaCC CaCC CaC CC CDD Interpretation InterpretationHighest quality, Extremely strongHighest quality, Extremely strongH
45、igh qualityHigh qualityStrong payment capacityStrong payment capacityAdequate payment capacityAdequate payment capacityLikely to fulfill, ongoing uncertaintyLikely to fulfill, ongoing uncertaintyHigh risk obligationHigh risk obligationCurrent vulnerability to defaultCurrent vulnerability to defaultI
46、n bankruptcy or default, or other In bankruptcy or default, or other marked shortcomingmarked shortcoming I In nv ve es st tmme en nt t GG. . S Sp pe ec cu ul la at ti iv ve e GGr ra ad de eClasses of credit ratingn nIssuer credit ratings(obligor rating): the rating is an Issuer credit ratings(oblig
47、or rating): the rating is an opinion on the obligors overall capacity to meet its opinion on the obligors overall capacity to meet its financial obligations. Including counterparty ratings, financial obligations. Including counterparty ratings, corporate credit ratings, and sovereign credit ratingsc
48、orporate credit ratings, and sovereign credit ratingsn nIssue-specific credit ratings(facility rating): an opinion Issue-specific credit ratings(facility rating): an opinion specific to a particular liability of the company. specific to a particular liability of the company. Long-term credits vs. Sh
49、ort-term credits Long-term credits vs. Short-term credits In rating a specific issue the attributes of the issuer, In rating a specific issue the attributes of the issuer, as well as the specific terms of the issue, the quality of as well as the specific terms of the issue, the quality of the collat
50、eral, and the creditworthiness of the the collateral, and the creditworthiness of the guarantors, are taken into account.guarantors, are taken into account.Power of ratingn nCredit ratings, especially those of S&P and Credit ratings, especially those of S&P and Moodys, are widely accepted by market
51、Moodys, are widely accepted by market participants and regulatory agencies. participants and regulatory agencies. n nRequired by their regulators to hold investment Required by their regulators to hold investment grade bonds, FIs use the ratings of credit grade bonds, FIs use the ratings of credit a
52、gencies to determine which bonds are of agencies to determine which bonds are of investment grade.investment grade.n nCredit ratings determine the credit risk spread of Credit ratings determine the credit risk spread of the rated bond, and therefore the financial cost of the rated bond, and therefor
53、e the financial cost of bond issuer. bond issuer. n nGreat impact of rating migration(downgrade) on Great impact of rating migration(downgrade) on capital market, especially issuer sidecapital market, especially issuer sideIndependence of credit ratingn nIndependence from issuersIndependence from is
54、suersn nImportance of independence Importance of independence n nKey to serving and protecting the interest of investorKey to serving and protecting the interest of investorn nKey to providing unbiased evaluations on Key to providing unbiased evaluations on creditworthinesscreditworthinessn nKey to
55、assuring the power of agencies is not abused. Key to assuring the power of agencies is not abused. n nKey to maintaining the credibility and therefore the Key to maintaining the credibility and therefore the survival of rating agencies themselvessurvival of rating agencies themselvesn nDoubt and deb
56、ate due to existing payment structure: Doubt and debate due to existing payment structure: Although their primary commitment is to serving the Although their primary commitment is to serving the investment community, the rating agencies are, in fact, investment community, the rating agencies are, in
57、 fact, paid primarily by issuers.paid primarily by issuers.n nFED New York study(Cantor and Packer 1994,4) shows FED New York study(Cantor and Packer 1994,4) shows this payment arrangement has not, for the most part, this payment arrangement has not, for the most part, eroded the agencies credibilit
58、y.eroded the agencies credibility.Moodys Rating Analysis of an Industrial Company Issue StructureCompany StructureOperational/FinancialPositionManagement QualityIndustry/Regulatory TrendsSovereign/Macroeconomic AnalysisS&Ps debt rating process Request RatingAssign Analytical TeamConduct Basic Resear
59、chMeet IssuerRating committeeMeetingIssue RatingSurveillanceAppeals processRating focus of S&P Business Risk Business Riskn nIndustry characteristicsIndustry characteristics (Highest weighted)(Highest weighted)n nCompetitive position Competitive position (e.g.)Marketing(e.g.)Marketing Technology Tec
60、hnology Efficiency Efficiency (Major focus)(Major focus)n n Management Management Financial Risk Financial Riskn nFinancial characteristicsFinancial characteristicsn nFinancial policyFinancial policyn nProfitabilityProfitabilityn nCapital structureCapital structuren nCash flow protectionCash flow pr
61、otectionn nFinancial flexibilityFinancial flexibility2.3.2 Internal ratingn nWhy internal ratingWhy internal ratingn nOCC modelOCC modeln nBank tailored rating systemBank tailored rating systemn nAn example of extended finer loan rating system An example of extended finer loan rating system and bond
62、 rating mappingand bond rating mappingWhy internal rating?n nExternal rating is traditionally restrained to public External rating is traditionally restrained to public bonds, bond rating, rather than loan ratingbonds, bond rating, rather than loan ratingn nCredit (loan) allocationCredit (loan) allo
63、cationn nCredit (loan) pricingCredit (loan) pricingn nLoss provision(reserve)Loss provision(reserve)n nCapital (Economical vs. Regulatory)Capital (Economical vs. Regulatory)n nImportant part of credit analysis and risk Important part of credit analysis and risk managementmanagementOCC modeln nOne of
64、 the oldest loan rating systemsOne of the oldest loan rating systemsn nDeveloped by U.S.Office of the Comptroller of the Developed by U.S.Office of the Comptroller of the Currency(OCC)Currency(OCC)n nUsed by regulators and bankers to assess the adequacy Used by regulators and bankers to assess the a
65、dequacy of their loan loss reserves.of their loan loss reserves.n nLoan categories and the required loss reserve Loan categories and the required loss reserve High-quality rating: High-quality rating: Pass/Performing 0% Pass/Performing 0% Low-quality rating: Low-quality rating: Other assets especial
66、ly mentioned(OAEM) 0% Other assets especially mentioned(OAEM) 0% Substandard assets 25% Substandard assets 25% Doubtful assets 50% Doubtful assets 50% Loss assets 100% Loss assets 100%Bank tailored rating systemn n60% 60% of U.S. bank holding companies have of U.S. bank holding companies have develo
67、ped internal rating systems for loans on a developed internal rating systems for loans on a 1-9 or 1-10 scale, including the top 50.1-9 or 1-10 scale, including the top 50.n nThe OCC pass/performing grade is finely The OCC pass/performing grade is finely subdivided into 6 different categories to bet
68、ter subdivided into 6 different categories to better reflect that some pass or performing loans will reflect that some pass or performing loans will still have a chance go into default.still have a chance go into default.An example of extended finer loan rating system and bond rating mapping Bond Ra
69、ting Score Risk Level Bond Rating Score Risk Level Bond Rating Score Risk Level Bond Rating Score Risk Level AAA 1 Minimal B 6 Management AAA 1 Minimal B 6 Management Attention Attention AA 2 Modest CCC 7 Special AA 2 Modest CCC 7 Special mention(OAEM) mention(OAEM) A 3 Average CCC 8 Substandard A 3
70、 Average CCC 8 Substandard BBB 4 Acceptable CC/C 9 Doubtful BBB 4 Acceptable CC/C 9 Doubtful BB 5 Acceptable D 10 Loss BB 5 Acceptable D 10 Loss With care With care 2.4 Credit Scoring Modelsn n2.4.1 Introduction2.4.1 Introductionn n2.4.2 Linear probability model and Logit model2.4.2 Linear probabili
71、ty model and Logit modeln n2.4.3 Linear discriminant analysis2.4.3 Linear discriminant analysisn n2.4.4 Problems of CSMs2.4.4 Problems of CSMs 2.4.1 Introductionn nWhat are credit scoring models?What are credit scoring models?n nUsesUsesn nTypes Types n nProcessProcessWhat are credit scoring models?
72、n nCSMs are quantitative models that use observed CSMs are quantitative models that use observed borrower characteristics either to calculate a borrower characteristics either to calculate a “score” representing the applicants probability of “score” representing the applicants probability of default
73、 or to sort borrowers into different default default or to sort borrowers into different default risk classes. risk classes. Usesn nCSMs enable FIs to:CSMs enable FIs to: 1. Numerically establish which factors are 1. Numerically establish which factors are important in explaining default riskimporta
74、nt in explaining default risk 2.Evaluate the relative degree or importance of 2.Evaluate the relative degree or importance of these factorsthese factors 3. Improve the pricing of default risk (loans and 3. Improve the pricing of default risk (loans and bonds)bonds) 4. Be better able to screen out ba
75、d loan applicants 4. Be better able to screen out bad loan applicants 5. Be in a better position to calculate any reserves 5. Be in a better position to calculate any reserves needed to meet expected future loan losses.needed to meet expected future loan losses.Typesn nLinear probability modelLinear
76、 probability modeln nLogit modelLogit modeln nLinear discriminant analysisLinear discriminant analysisProcess1. Identify objective economic and financial 1. Identify objective economic and financial measures of risk for any particular class of measures of risk for any particular class of borrower:bo
77、rrower: Consumer debt: income, assets, age, Consumer debt: income, assets, age, occupation, and location.occupation, and location. Commercial debt: cash flow information, Commercial debt: cash flow information, financial rations, etcfinancial rations, etc2. Specify an appropriate statistic technique
78、 to 2. Specify an appropriate statistic technique to quantify or score the default risk probability of quantify or score the default risk probability of default risk classification.default risk classification. Linear probability models, Linear probability models, Logit models Logit models Linear dis
79、criminant analysis Linear discriminant analysis2.4.2 Linear probability models and Logit modelsn nUsing past data, such as financial ratios(XUsing past data, such as financial ratios(Xij ij), as inputs into a model ), as inputs into a model to explain repayment experience on old loans.to explain rep
80、ayment experience on old loans.n nDividing old loans(i) into two observational groups: Default(ZDividing old loans(i) into two observational groups: Default(Zi i =1) =1) and Non-default(Zand Non-default(Zi i =0)=0)n nUsing linear regression to estimate the model:ccUsing linear regression to estimate
81、 the model:cc n n Z Zi i = = t t i i X Xij ij+error +error j j=1=1 Where Where i i is the estimated importance of the jth variable in is the estimated importance of the jth variable in explaining past repayment experienceexplaining past repayment experiencen nThen, we take these estimated Then, we t
82、ake these estimated i is and multiply them by the s and multiply them by the observed Xobserved Xij ij for a prospective borrower, we can derive an expected for a prospective borrower, we can derive an expected value of Zvalue of Zi i for the prospective borrower.The value of Z for the prospective b
83、orrower.The value of Zi i can be can be interpreted as the probability of default for the borrower. interpreted as the probability of default for the borrower. n nIts major shortcoming is that ZIts major shortcoming is that Zi i can often lie outside the interval 0 can often lie outside the interval
84、 0 to 1. This shortcoming can be overcome by to 1. This shortcoming can be overcome by logit modellogit model. .2.4.3 Linear discriminant analysisn nDividing borrowers into high or low default risk classes contingent Dividing borrowers into high or low default risk classes contingent on their observ
85、ed characteristics (Xon their observed characteristics (Xij ij) )n nAltmans discriminant function for public traded manufacturing Altmans discriminant function for public traded manufacturing firms in the US:firms in the US: Z=1.2 Z=1.2 X X1 1+1.4 X+1.4 X2 2+3.3 X+3.3 X3 3+0.6 X+0.6 X4 4+1.0 X+1.0 X
86、5 5 X X1 1=working capital/total assets ratio=working capital/total assets ratio X X2 2=Retained earnings/total assets ratio=Retained earnings/total assets ratio X X3 3=Earnings before interest and taxes /total assets ratio=Earnings before interest and taxes /total assets ratio X X4 4=Market value o
87、f equity/book value of long-term debt ratio=Market value of equity/book value of long-term debt ratio X X5 5=Sales/total assets ratio=Sales/total assets ration nZ serves as an indicator of default risk, the higher the Z value, the Z serves as an indicator of default risk, the higher the Z value, the
88、 lower the probability that the borrower will default.lower the probability that the borrower will default.n nAccording to Altmans credit scoring model, any firm with a Z score According to Altmans credit scoring model, any firm with a Z score less than 1.81 should be placed in the high default risk
89、 class.less than 1.81 should be placed in the high default risk class.2.4.3 Problems of these traditional models 1. Past(historic) data, rather than financial 1. Past(historic) data, rather than financial market data, therefore backward-lookingmarket data, therefore backward-looking 2. Rely on stati
90、stics techniques rather than on 2. Rely on statistics techniques rather than on modern financial theorymodern financial theory 3. Default-focus, rather than the whole credit 3. Default-focus, rather than the whole credit changing processchanging process More Problems : See A: 280More Problems : See
91、A: 280Termsn nCredit/default /counterparty Credit/default /counterparty /settlement/sovereign/ /settlement/sovereign/ country/ credit migration riskcountry/ credit migration riskn nInformation asymmetryInformation asymmetryn nAgency problemAgency problemn n5Cs of expert system5Cs of expert systemn n
92、Fat tailFat tailn nExpected lossExpected lossn nUnexpected lossUnexpected lossn nProbability of defaultProbability of defaultn nLoss given default/recovery Loss given default/recovery rateraten nExternal rating(credit rating)External rating(credit rating)n nInvestment gradeInvestment graden nSpecula
93、tive gradeSpeculative graden nObligor ratingObligor ratingn nFacility ratingFacility ratingn nCredit scoringCredit scoringQuestionsn nWhat is your understanding of credit risk in the context of modern What is your understanding of credit risk in the context of modern finance?finance?n nWhat are the
94、major characteristics of credit risk and their What are the major characteristics of credit risk and their implication to credit risk management?implication to credit risk management?n nDiagram the actual PDF of credit loss, and compare with normal Diagram the actual PDF of credit loss, and compare
95、with normal distribution.distribution.n nWhat are the major differences between traditional credit risk What are the major differences between traditional credit risk management and modern credit risk managementmanagement and modern credit risk managementn nWhat are the traditional expert system of
96、credit analysis and it What are the traditional expert system of credit analysis and it major problems?major problems?n nWhat is the basic mission of credit rating agencies?What is the basic mission of credit rating agencies?n nWhy are rating agencies are so powerful in financial markets?Why are rat
97、ing agencies are so powerful in financial markets?n nWhy is independence of rating is so important?Why is independence of rating is so important?n nWhat is OCC model?What is OCC model?n nWhat is the basic process of credit scoring?What is the basic process of credit scoring?n nWhat are the major sho
98、rtcomings of credit scoring models?What are the major shortcomings of credit scoring models?Suggested Readingn nChapter 11, Financial Institutions ManagementChapter 11, Financial Institutions Managementn nChapter 7, Risk Management, by Michel CrouhyChapter 7, Risk Management, by Michel Crouhyn nChap
99、ter 2, Credit Risk Measurement, by Anthony Chapter 2, Credit Risk Measurement, by Anthony SaundersSaunders Lecture 113.Credit analysis and credit risk measuring: Modern approachesn n3.1 3.1 IntroductionIntroductionn n3.2 The term structure of credit risk approach3.2 The term structure of credit risk
100、 approachn n3.3 Mortality rate approach3.3 Mortality rate approachn n3.4 RAROC model3.4 RAROC modeln n3.5 Option model (including the KMV credit 3.5 Option model (including the KMV credit monitor model)monitor model)n n3.6 CreditMetrics3.6 CreditMetrics3.1 Introductionn nModern financial theories ar
101、e appliedModern financial theories are appliedn nFinancial market data to make inferences about default Financial market data to make inferences about default probabilities on debt and loan instruments probabilities on debt and loan instruments n nThese models are most relevant in evaluating loans t
102、o larger These models are most relevant in evaluating loans to larger borrowers in the corporate sector.borrowers in the corporate sector.n nFocus of a great deal of current research Focus of a great deal of current research n nPortfolio effect can be taken into accountPortfolio effect can be taken
103、into accountn nMore meaningful in credit pricing, rationing More meaningful in credit pricing, rationing n nBetter serve financial innovations such as credit derivative, Better serve financial innovations such as credit derivative, structured finance, loan sales, securitizationstructured finance, lo
104、an sales, securitizationn nTypes: Term Structure Derivation Model, Mortality Derivation Types: Term Structure Derivation Model, Mortality Derivation model, KMV model, Creditmetrics, Creidt Risk+, RAROC model, KMV model, Creditmetrics, Creidt Risk+, RAROC 3.2 Term Structure Derivation of Credit Riskn
105、 nExtract (expected) default probabilities of a specific Extract (expected) default probabilities of a specific grade bond or loan from current term structure of grade bond or loan from current term structure of interest rates, more specifically, the risk premiums interest rates, more specifically,
106、the risk premiums inherent in the current structure of yields on corporate inherent in the current structure of yields on corporate debt or loans to similar risk-rated borrowers. debt or loans to similar risk-rated borrowers. n nTerms structure(or yield curve )of interest rates Terms structure(or yi
107、eld curve )of interest rates compares the market yields or interest rates on compares the market yields or interest rates on securities, assuming the all characteristics( default securities, assuming the all characteristics( default risk, coupon rate, etc.) except maturity are the risk, coupon rate,
108、 etc.) except maturity are the same.(P190)same.(P190)n n(Credit) Risk premium is the yield difference between a (Credit) Risk premium is the yield difference between a specific grade of bond and risk-free treasury bonds with specific grade of bond and risk-free treasury bonds with the same maturity,
109、 it is the (market)yield the same maturity, it is the (market)yield compensation for credit risk, thus analysis of risk compensation for credit risk, thus analysis of risk premium will reveal the market recognition ( reflection, premium will reveal the market recognition ( reflection, assessment) of
110、 credit risk level. assessment) of credit risk level. Corporate bonds(grade B)T-bonds15.8%10%18%11%Maturity(years)Yield(%)Credit risk premium of 2-year, B-grade C-bonds is 7%Credit risk premiumof 1-year, B-gradeC-bonds is 5.8%12Deriving default probability from term structure (one-period debt model)
111、n nAssume:Assume: (1) Expected return on the loan: p(1+k)+(1-p) (1+k) (1) Expected return on the loan: p(1+k)+(1-p) (1+k) k : Rate of return on the loan (contractually promised) k : Rate of return on the loan (contractually promised) p: probability of full repayment;1-p:Default probabilityp: probabi
112、lity of full repayment;1-p:Default probability : recovery rate given default; 1-:Loss given default : recovery rate given default; 1-:Loss given default (2) Return of credit risk-free Treasury security: 1+i (2) Return of credit risk-free Treasury security: 1+in nFIs require: (1)=(2) when they would
113、just be FIs require: (1)=(2) when they would just be indifferent between the two investment opportunitiesindifferent between the two investment opportunities p(1+k)+(1-p) (1+k)= 1+i p(1+k)+(1-p) (1+k)= 1+in nDefault probabilityDefault probability of the loan (1-p): of the loan (1-p):n nIf =0 is assu
114、med: p =(1+i)/ (1+k); 1-p=(k-i)/(1+k)If =0 is assumed: p =(1+i)/ (1+k); 1-p=(k-i)/(1+k)n nDefault probability on a multi-period case (P 284)Default probability on a multi-period case (P 284) (1+i)-(1+k) (1+i)-(1+k)(1+k) (1+k)(1+k) (1+k)p=p=ExampleSuppose:i=10%, k=15.8% Suppose:i=10%, k=15.8% (Credit
115、 risk premium=k-i=5.8%)(Credit risk premium=k-i=5.8%)If=0, p =(1+i)/ (1+k)=1.100/1.158=0.95If=0, p =(1+i)/ (1+k)=1.100/1.158=0.95If=0.5If=0.5 (1+i)- (1+k) (1+i)- (1+k) (1+k) (1+k) (1+k) (1+k) 1-p=0.1 1-p=0.1 p=p=0.90=0.90Determinants of credit risk premium (1+i) (1+i) (+p-p) (+p-p) The higher defaul
116、t probability (1-p), the higher The higher default probability (1-p), the higher credit risk credit risk premium(k-ipremium(k-i).). andand p are perfect substitutes for each other in p are perfect substitutes for each other in this simple framework. That is a loan with this simple framework. That is
117、 a loan with collateral backing of =0.7 and p=0.8 would have collateral backing of =0.7 and p=0.8 would have the same required risk premium as one with the same required risk premium as one with =0.8 and p=0.7. An increase in collateral =0.8 and p=0.7. An increase in collateral isis a a direct subst
118、itute for an increase in default direct substitute for an increase in default risk(i.erisk(i.e., a decline in p)., a decline in p).- (1+i)- (1+i)k-i=k-i=Advantage and Disadvantagen nAdvantage: forward-looking and based on market Advantage: forward-looking and based on market expectationexpectationn
119、nDisadvantage: liquid market requirement for both Disadvantage: liquid market requirement for both Treasury bonds and corporate discount bondsTreasury bonds and corporate discount bonds3.3 Mortality Rate Derivation of Credit Riskn nDeriving the default rate from the historic or past Deriving the def
120、ault rate from the historic or past default risk experience, the default risk experience, the mortality ratesmortality rates, of bonds , of bonds and loans of a similar quality(in the same grade)and loans of a similar quality(in the same grade)n nSimilar to the process employed by insurance Similar
121、to the process employed by insurance companies to price policies. The probability of default is companies to price policies. The probability of default is estimated from past data on defaults.estimated from past data on defaults.n nMarginal mortality rate (MMR)Marginal mortality rate (MMR): The prob
122、ability of a : The probability of a bond or a loan dying (defaulting) in any given year bond or a loan dying (defaulting) in any given year after issuanceafter issuance Total value of B bonds defaulting in year 1 of issueTotal value of B bonds defaulting in year 1 of issue Total value of B bonds out
123、standing in year 1 of issue Total value of B bonds outstanding in year 1 of issue Total value of B bonds defaulting in year 2 of issue Total value of B bonds defaulting in year 2 of issue Total value of B bonds outstanding in year 2 of issue Total value of B bonds outstanding in year 2 of issue (adj
124、usted for defaults, calls, sinking fund redemptions and (adjusted for defaults, calls, sinking fund redemptions and maturities in the prior year) maturities in the prior year)MMRMMR1 1=MMRMMR2 2= n nMMR table:P288: 933 rated corporate bonds over MMR table:P288: 933 rated corporate bonds over the 197
125、1-2000 periodthe 1971-2000 period It can be observed that the lower the rating of It can be observed that the lower the rating of the bond, the higher that mortality rates.the bond, the higher that mortality rates.n nMMR curve and its shapeMMR curve and its shapen nProblems: Problems: (1)Based on hi
126、storic data, Historic, backward- (1)Based on historic data, Historic, backward-lookinglooking (2)The estimates of default rates are sensitive to (2)The estimates of default rates are sensitive to the period of observation, the number of issues the period of observation, the number of issues and the
127、relative size of issues in each investment and the relative size of issues in each investment gradegrade3.4 RAROC Modelsn nRisk adjusted return on capitalRisk adjusted return on capital, one of the more , one of the more widely used models, pioneered by Banker the Trust in widely used models, pionee
128、red by Banker the Trust in 1998 and gaining popularity ever since1998 and gaining popularity ever sincen nThe essential idea behind RAROC:rather than The essential idea behind RAROC:rather than evaluating the actual or contractually promised annual evaluating the actual or contractually promised ann
129、ual ROA on a loan, balance expected interest and fee ROA on a loan, balance expected interest and fee income of a loan against its expected risk, through income of a loan against its expected risk, through dividing annual loan income by some measure of dividing annual loan income by some measure of
130、asset(or loan) risk, or what is often called capital at asset(or loan) risk, or what is often called capital at risk, since (unexpected) loan losses have to be written risk, since (unexpected) loan losses have to be written off against an FIs capital:off against an FIs capital: One year income on a
131、loan One year income on a loan Loan risk or capital at risk Loan risk or capital at riskRAROC=RAROC= n nA loan is approved only if RAROC is sufficiently A loan is approved only if RAROC is sufficiently high relative to a benchmark return on high relative to a benchmark return on capital(ROE) for the
132、 FI where ROE measures the capital(ROE) for the FI where ROE measures the return stockholders require on their equity return stockholders require on their equity investment in the FI.investment in the FI. (Comments: In this case, RAROC is used to (Comments: In this case, RAROC is used to help loan d
133、ecision.)help loan decision.)n nThe key task: how to estimate the loan risk?The key task: how to estimate the loan risk? - Using credit (yearly) VaR of loan - Using credit (yearly) VaR of loan Recall duration modeln ndP = -DdR/(1+R)P = -(MD) (dR) (P) dP = -DdR/(1+R)P = -(MD) (dR) (P) n nGiven a risk
134、 factor change(dR, like interest rate rise) Given a risk factor change(dR, like interest rate rise) the change of bond value(dP) is the product of MD, dR the change of bond value(dP) is the product of MD, dR and P.and P.n nIncorporates duration approach to estimate worst case Incorporates duration a
135、pproach to estimate worst case loss in value of the loan:loss in value of the loan: D D D DL = -DL = -DL L L ( L (D D D DR/(1+R),R/(1+R), or or D D D DL = -MDL = -MDL L L L D D D DRR, since MD, since MDL L= D= DL L/(1+R)/(1+R)n nHere, L denotes loan size, Here, L denotes loan size, D DR is an estima
136、te of the R is an estimate of the worst change in credit risk premiums for the loan class worst change in credit risk premiums for the loan class over the past year. over the past year. n nHow to define the worst change in credit risk How to define the worst change in credit risk premiums? We turn t
137、o confidence level and VaR model.premiums? We turn to confidence level and VaR model. Recall VaR model (Market risk) VaR = P S DR$ value of your positionUnit sensitivity of your positiongiven a unit change of risk factorBad Changes (Volatility,PDF)of risk factor $1 positions volatility Credit VaR Va
138、R = L S DR$ $ value ofvalue of loan sizeloan sizeUnit sensitivity of loan Unit sensitivity of loan position given a unit position given a unit change of risk factor, change of risk factor, credit risk premium. credit risk premium. S=-MDS=-MDL L =-D =-DL L/(1+R)/(1+R)Bad Changes Bad Changes (Volatili
139、ty,PDF)(Volatility,PDF)Of risk factor,Of risk factor,credit risk premium credit risk premium $1 loan positions volatility $1 loan positions volatility Credit VaR = L (- DCredit VaR = L (- DL L /(1+R) ) /(1+R) ) D DR at a given confidence levelR at a given confidence levelExamplen nSuppose: DSuppose:
140、 DL L =2.7ys, L=$1million, R=10%, and =2.7ys, L=$1million, R=10%, and projected 1-year spread(0.2%) plus fee(0.1) is $3000projected 1-year spread(0.2%) plus fee(0.1) is $3000n nTo evaluate the credit risk of a loan to a AAA borrower, To evaluate the credit risk of a loan to a AAA borrower, assume th
141、ere are currently 400 publicly traded bonds assume there are currently 400 publicly traded bonds in that class. Rearrange and plot in the frequency in that class. Rearrange and plot in the frequency curve the actual changes in the credit risk premiums curve the actual changes in the credit risk prem
142、iums (R(Ri i-R-Rg g) on each of these bonds for the past year from ) on each of these bonds for the past year from the largest fall (-2%) to the biggest increase (3.5%).the largest fall (-2%) to the biggest increase (3.5%).n nThe 99% worst-case scenario is chosen, i.e., only 4 out The 99% worst-case
143、 scenario is chosen, i.e., only 4 out of 400 had risk premium increases the 99% worst of 400 had risk premium increases the 99% worst case. Suppose in our example that is equal to 1.1%case. Suppose in our example that is equal to 1.1%n nVaR =L (- DVaR =L (- DL L /(1+R) ) /(1+R) ) D DR (99% confidenc
144、e level) R (99% confidence level) = $1million(-2.7/(1+ 10% ) 1.1% at 99% CL = $1million(-2.7/(1+ 10% ) 1.1% at 99% CL =-$2,700 at 99% confidence level =-$2,700 at 99% confidence leveln nThe loans RAROC=Income /Loan riskThe loans RAROC=Income /Loan risk = $3000/ $2,700 =11.1% = $3000/ $2,700 =11.1%An
145、other way One year income per dollar loaned One year income per dollar loaned Unexpected default rateLoss given default Unexpected default rateLoss given defaultSuppose expected income per dollar lent is 0.3 Suppose expected income per dollar lent is 0.3 cents, the 99cents, the 99thth percentile his
146、toric default rate for percentile historic default rate for borrowers of this type is 4% and the LGD is 80%borrowers of this type is 4% and the LGD is 80% RAROC=0.003/(0.004 RAROC=0.003/(0.0040.0320.032)=9.375%)=9.375%To do this, very good loan default databases are To do this, very good loan defaul
147、t databases are needed.needed.RAROC=RAROC=3.5 Option Models of Default Riskn nTheoretical frameworkTheoretical framework Recent recognition following the pioneering work Recent recognition following the pioneering work of Merton, Black, and Scholes: When a firm raises of Merton, Black, and Scholes:
148、When a firm raises funds by issuing bonds or increasing its bank funds by issuing bonds or increasing its bank loans, it holds a very valuable default or loans, it holds a very valuable default or repayment option, due to limited liability for repayment option, due to limited liability for equity ho
149、lders.equity holders. A: The Borrowers payoff from loans A: The Borrowers payoff from loans B: The debtholders payoff from loans B: The debtholders payoff from loans A A(Assets)(Assets) A A(Assets)(Assets)Payoff to Stockholders:Payoff to Stockholders: Max(0, A-B) Max(0, A-B) Payoff to Loan-holders:P
150、ayoff to Loan-holders:Min(B, A)Min(B, A)- -S SB(debt)B(debt)A A1 1A A1 1A A2 2A A2 20 00 0B B Apply the option valuation model to the calculation of Apply the option valuation model to the calculation of default risk premiums(and therefore default probability) default risk premiums(and therefore def
151、ault probability) n nThe option valuation formula: The option valuation formula: See Textbook 293 formula (4)See Textbook 293 formula (4) Value of the loan = F(B, A, , i, T, ) Value of the loan = F(B, A, , i, T, )n nWritten in terms of a yield spread:Written in terms of a yield spread: The equilibri
152、um default risk premium that the borrower The equilibrium default risk premium that the borrower should be charged: k-i= f(B, A, , i, T, )should be charged: k-i= f(B, A, , i, T, )Time to maturityDebt outstanding (exercise price)Risk-free interest rateMarket value of firm assets(underlying asset)Asse
153、t risk: volatility of A For detailed formula see textbook 293For detailed formula see textbook 294 n nProblem: Neither the market value of firms asset (A) Problem: Neither the market value of firms asset (A) nor its volatility() is directly observed nor its volatility() is directly observed n nKMV a
154、pproach to the problem: Using an option pricing KMV approach to the problem: Using an option pricing model to extract the implied market value of assets model to extract the implied market value of assets and its volatility of a given firms asset.and its volatility of a given firms asset.n nThe KMV
155、model uses the value of equity in a firm (from The KMV model uses the value of equity in a firm (from a stockholders perspective) as equivalent to holding a a stockholders perspective) as equivalent to holding a call on the assets of the firm(with the amount of debt call on the assets of the firm(wi
156、th the amount of debt borrowed acting similar to the exercise price of the call borrowed acting similar to the exercise price of the call option). Then, firms equity value E=f(B, A, , i, T, ); option). Then, firms equity value E=f(B, A, , i, T, ); n nSince E=A-B, firm equitys volatility should refle
157、ct the Since E=A-B, firm equitys volatility should reflect the leverage adjusted volatility of firm assets, leverage adjusted volatility of firm assets, E E =g(=g( ) )n nUnknown A andcan be worked out by solving the two Unknown A andcan be worked out by solving the two equations. These are called im
158、plied A and .equations. These are called implied A and . B BAsset market value (A) Asset market value (A) $ $Contractual amount of Contractual amount of current obligationscurrent obligations(Default point)(Default point)Probability of default Probability of default (EDF)(EDF) Distance from default
159、Distance from defaultFrequency distributionFrequency distributionof asset market valuesof asset market valuesAt time 1At time 1TimeTime0 0 1 1 A A in $in $ - - B Bn nEDF(Expected Default Frequency) EDF(Expected Default Frequency) n nand Distance from Defaultand Distance from DefaultExamplen nSuppose
160、: A=$100m at time 0, B=$80m,= $12.12m Suppose: A=$100m at time 0, B=$80m,= $12.12m Normal distribution of assets valueNormal distribution of assets valuen nThen, Then, Distance to default(DTD)Distance to default(DTD)=(B-A)/=(B-A)/ = (100-80)/12.12=1.65 = (100-80)/12.12=1.65n nThis also means 5% prob
161、ability of the firm going into This also means 5% probability of the firm going into distress over the next year(by time 1): distress over the next year(by time 1): Expected Default Frequency(EDF)Expected Default Frequency(EDF) = 5% = 5%n nIt is claimed that EDF score outperforms both Z It is claime
162、d that EDF score outperforms both Z score-type mode and S&P rating changes as score-type mode and S&P rating changes as predictors of corporate failure and distress and predictors of corporate failure and distress and thus give better “early warning” of impending thus give better “early warning” of
163、impending default.default.n nOne reason for this is that the KMV score is One reason for this is that the KMV score is extracted from stock market data that is highly extracted from stock market data that is highly sensitive t new information about a firms future sensitive t new information about a
164、firms future prospects.prospects.n nKMV provides monthly EDFs for over 6,000 U.S. KMV provides monthly EDFs for over 6,000 U.S. companies and 20,000 companies panies and 20,000 companies worldwide. 3.6 Creditmetrics Modeln nIntroduced in 1997 by J.P.Morgan and its co-Introduced in 1997 by J.P.Morgan
165、 and its co-sponsors(Bank of America, Union Bank of sponsors(Bank of America, Union Bank of Switzerland, etc)Switzerland, etc)n nA value at risk framework to apply to the A value at risk framework to apply to the valuation and risk of nontradable assets such as valuation and risk of nontradable asse
166、ts such as loans and privately placed bonds.loans and privately placed bonds.n n“If next year (yearly VaR) is a bad year, how “If next year (yearly VaR) is a bad year, how much will I lose on my loans and loan portfolio?”much will I lose on my loans and loan portfolio?”n nVaR=P1.65 (at 95% confidenc
167、e level)VaR=P1.65 (at 95% confidence level)n nKey problem: market value(P) of the loan and its Key problem: market value(P) of the loan and its volatility() are not observedvolatility() are not observedSolution to the problemTo calculate a hypothetical P and for any non-To calculate a hypothetical P
168、 and for any non-tradable loan or bond and thus a VaR figure for tradable loan or bond and thus a VaR figure for individual loans and the loan portfolio using:individual loans and the loan portfolio using:n nAvailable data on a borrowers credit ratingAvailable data on a borrowers credit ratingn nThe
169、 probability of that rating changing (rate drift, The probability of that rating changing (rate drift, rate migration)over the next year(the rating rate migration)over the next year(the rating transition matrix)transition matrix)n nRecovery rates on defaulted loansRecovery rates on defaulted loansn
170、nYield spreads in the bond marketYield spreads in the bond marketProcessn nRating migration (Rating transition matrix)Rating migration (Rating transition matrix)n nValuation and PDF of loan valuesValuation and PDF of loan valuesn nCalculation of VaRCalculation of VaR Assuming normal distribution Ass
171、uming normal distribution Assuming actual distribution Assuming actual distributionExamplen n5-5-year, fixed-rate loan of $100million with 6% year, fixed-rate loan of $100million with 6% annual interest rate, rated BBBannual interest rate, rated BBBn nRating migration:Rating migration:One-year trans
172、ition probabilities for BBB-rated borrowerOne-year transition probabilities for BBB-rated borrowern nValuationValuationn nCalculation of VaRCalculation of VaRVaR Calculations for the BBB LoanYear-End Probability New Loan Value Probability Difference of Value Probability WeightedYear-End Probability
173、New Loan Value Probability Difference of Value Probability WeightedRating of State,% Plus Coupon,$ Weighted Value,$ From Mean,$ Difference SquaredRating of State,% Plus Coupon,$ Weighted Value,$ From Mean,$ Difference SquaredAAA 0.02% $109.37 $0.02 $2.28 0.0010AAA 0.02% $109.37 $0.02 $2.28 0.0010AA
174、0.33 109.19 0.36 2.10 0.0146AA 0.33 109.19 0.36 2.10 0.0146A 5.95 108.66 6.47 1.57 0.1474A 5.95 108.66 6.47 1.57 0.1474BBB 86.93 107.55 93.49 0.46 0.1853BBB 86.93 107.55 93.49 0.46 0.1853BB 5.30 102.02 5.41 (5.06) 1.3592BB 5.30 102.02 5.41 (5.06) 1.3592B 1.17 98.10 1.15 (8.99) 0.9446B 1.17 98.10 1.1
175、5 (8.99) 0.9446CCC 0.12 83.64 1.10 (23.45) 0.6598 CCC 0.12 83.64 1.10 (23.45) 0.6598 Default 0.18 51.13 0.09 (55.96) 5.6358Default 0.18 51.13 0.09 (55.96) 5.6358 Mean=$107.09 Variance=8.94777 Mean=$107.09 Variance=8.94777 = Standard deviation=$2.99 = Standard deviation=$2.99 Assuming Normal 5% VAR =
176、 1.65 X Assuming Normal 5% VAR = 1.65 X =4.93 =4.93 Distribution 1% VAR = 2.33 X Distribution 1% VAR = 2.33 X $6.97 $6.97 Assuming Actual 5% VAR = 95% of actual distribution = $107.09-$102.02=$5.07 Assuming Actual 5% VAR = 95% of actual distribution = $107.09-$102.02=$5.07 Distribution* 1% VAR = 99%
177、 of actual distribution = $107.09 -$98.10=$8.99 Distribution* 1% VAR = 99% of actual distribution = $107.09 -$98.10=$8.99 * 5% VAR approximated by 6.77% VAR(i.e. 5.3%+ 1.17%+ 0.12%+ 0.18%) * 5% VAR approximated by 6.77% VAR(i.e. 5.3%+ 1.17%+ 0.12%+ 0.18%) 1% VAR approximated by 1.47% VAR(i.e. 1.17%+
178、 0.12%+ 0.18%) 1% VAR approximated by 1.47% VAR(i.e. 1.17%+ 0.12%+ 0.18%) Distribution of loan value 107.09Mean51.13109.37Value of loanProbabilityTermsn nTerm structure/yield Term structure/yield curvecurven nCredit risk Credit risk premium/credit premium/credit spreadspreadn nMarginal mortality Mar
179、ginal mortality rateraten nRAROCRAROCn nCredit VaRCredit VaRn nKMV modelKMV modeln nExpected default Expected default frequency (EDF)frequency (EDF)n nDistant to defaultDistant to defaultn nCreditmetrics modelCreditmetrics modelQuestionsn nHow do you derive default probability from term How do you d
180、erive default probability from term structure of bonds?structure of bonds?n nWhat are the major problems of term-structure What are the major problems of term-structure derivation model and mortality rate derivation derivation model and mortality rate derivation model?model?n nHow do you calculate R
181、AROC of a perspective How do you calculate RAROC of a perspective loan and use it in decision making?loan and use it in decision making?n nWhat is the theoretical framework of KMV model?What is the theoretical framework of KMV model?n nWhat are the basic ideas of creditmetrics model? What are the ba
182、sic ideas of creditmetrics model? Suggested Reading and Assigned Problemsn nSuggested Reading: Suggested Reading: Chapter 11, Financial Institutions Management Chapter 11, Financial Institutions Managementn nProblem set 3, part 1Problem set 3, part 1(Due date:April 22)(Due date:April 22) Questions and Problems: 24, 32, and34 Questions and Problems: 24, 32, and34See Page299-301, Financial Institutions See Page299-301, Financial Institutions ManagementManagement
