CreditValueatRiskChapter 18RiskManagementandFinanciallnstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 Credit Value at Risk Chapter 18 1
Rating Transitions One year rating transition probabilities arepublished by rating agenciesIf we assume that the rating transition in oneperiod is independent of that in other periods wecan calculate the rating transition for any period(see Appendix J and software)The “ratings momentum" phenomenon meansthat the independence assumption is notperfectly correct2RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Rating Transitions ⚫ One year rating transition probabilities are published by rating agencies. ⚫ If we assume that the rating transition in one period is independent of that in other periods we can calculate the rating transition for any period (see Appendix J and software) ⚫ The “ratings momentum” phenomenon means that the independence assumption is not perfectly correct Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 2
One-Year Rating TransitionMatrix (% probability, Moody's 1970-2010)Table18.1page401InitialRatingatyearendAAaBAaaBaCaaCa-CDefaultRatingBaaAaa90.428.920.620.010.030.000.000.000.00Aa1.0290.128.380.380.050.020.010.000.02A5.520.510.030.010.062.8290.880.110.060.19Baa0.050.194.7989.414.350.820.180.02Ba0.010.060.410.590.091.226.2283.437.97B5.320.010.040.140.3882.196.450.744.739.41Caa0.000.020.020.160.534.6716.7668.43Ca-C0.000.000.000.000.392.8510.6642.5643.54Default0.000.000.000.000.000.000.000.00100.003RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
One-Year Rating Transition Matrix (% probability, Moody’s 1970-2010) Table 18.1 page 401 Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 3 Initial Rating Aaa Aa A Baa Ba B Caa Ca-C Default Aaa 90.42 8.92 0.62 0.01 0.03 0.00 0.00 0.00 0.00 Aa 1.02 90.12 8.38 0.38 0.05 0.02 0.01 0.00 0.02 A 0.06 2.82 90.88 5.52 0.51 0.11 0.03 0.01 0.06 Baa 0.05 0.19 4.79 89.41 4.35 0.82 0.18 0.02 0.19 Ba 0.01 0.06 0.41 6.22 83.43 7.97 0.59 0.09 1.22 B 0.01 0.04 0.14 0.38 5.32 82.19 6.45 0.74 4.73 Caa 0.00 0.02 0.02 0.16 0.53 9.41 68.43 4.67 16.76 Ca-C 0.00 0.00 0.00 0.00 0.39 2.85 10.66 43.54 42.56 Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 Rating at year end
Five-YearRatingTransitionMatrix (calculatedfromone-yeartransitions)Table18.2page401InitialRatingatendAAaBAaaBaCaaCa-CDefaultRatingBaaAaa61.1229.997.700.890.210.050.010.000.03Aa28.700.250.193.4561.894.710.730.070.01A0.449.720.040.603.241.060.2465.7818.884.640.972.06Baa0.221.6960.9812.930.1316.38Ba0.070.4420.073.700.523.4018.2044.698.92B1.640.040.200.833.2713.2843.0511.4926.21Caa0.010.080.230.933.5216.8018.672.9356.84Ca-C0.000.020.060.311.395.896.782.4083.15Default0.000.000.000.000.000.000.000.00100.00RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull20124
Five-Year Rating Transition Matrix (calculated from one-year transitions) Table 18.2 page 401 Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 4 Initial Rating Aaa Aa A Baa Ba B Caa Ca-C Default Aaa 61.12 29.99 7.70 0.89 0.21 0.05 0.01 0.00 0.03 Aa 3.45 61.89 28.70 4.71 0.73 0.25 0.07 0.01 0.19 A 0.44 9.72 65.78 18.88 3.24 1.06 0.24 0.04 0.60 Baa 0.22 1.69 16.38 60.98 12.93 4.64 0.97 0.13 2.06 Ba 0.07 0.44 3.40 18.20 44.69 20.07 3.70 0.52 8.92 B 0.04 0.20 0.83 3.27 13.28 43.05 11.49 1.64 26.21 Caa 0.01 0.08 0.23 0.93 3.52 16.80 18.67 2.93 56.84 Ca-C 0.00 0.02 0.06 0.31 1.39 5.89 6.78 2.40 83.15 Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 Rating at end
One-Month Rating TransitionMatrix(calculatedfromone-yeartransitions)Table18.3page401InitialRatingatmonthendAAaBAaaBaCaaCa-CDefaultRatingBaaAaa99.160.820.020.000.000.000.000.000.00Aa0.0999.120.770.010.000.000.000.000.00A0.510.040.010.000.000.000.000.2699.180.010.020.01Baa0.000.4499.050.410.060.00Ba0.000.000.020.590.030.010.0998.460.79B0.000.000.010.020.5398.320.700.070.36Caa0.000.000.000.010.021.0196.790.671.48Ca-C0.000.000.000.000.040.281.534.9293.23Default0.000.000.000.000.000.000.000.00100.005RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
One-Month Rating Transition Matrix (calculated from one-year transitions) Table 18.3 page 401 Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 5 Initial Rating Aaa Aa A Baa Ba B Caa Ca-C Default Aaa 99.16 0.82 0.02 0.00 0.00 0.00 0.00 0.00 0.00 Aa 0.09 99.12 0.77 0.01 0.00 0.00 0.00 0.00 0.00 A 0.00 0.26 99.18 0.51 0.04 0.01 0.00 0.00 0.00 Baa 0.00 0.01 0.44 99.05 0.41 0.06 0.02 0.00 0.01 Ba 0.00 0.00 0.02 0.59 98.46 0.79 0.03 0.01 0.09 B 0.00 0.00 0.01 0.02 0.53 98.32 0.70 0.07 0.36 Caa 0.00 0.00 0.00 0.01 0.02 1.01 96.79 0.67 1.48 Ca-C 0.00 0.00 0.00 0.00 0.04 0.28 1.53 93.23 4.92 Default 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100.00 Rating at month end
Credit VaR (page 321) Can be defined analogously to MarketRiskVaRA one year credit VaR with a 99.9%confidence is the loss level that we are99.9% confidentwill not be exceeded overone year6RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 Credit VaR (page 321) ⚫ Can be defined analogously to Market Risk VaR ⚫ A one year credit VaR with a 99.9% confidence is the loss level that we are 99.9% confident will not be exceeded over one year 6
Vasicek's Model (Equation 18.1, page 402)Foralargeportfolioof loans,eachofwhichhasa probability of O(T) of defaulting by time T thedefault rate that will not be exceeded at the X%confidenceleveljsN-I[Q(T)]+VpN-'(X)N/1-pWhere p is the Gaussian copula correlation7RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 Vasicek’s Model (Equation 18.1, page 402) ⚫ For a large portfolio of loans, each of which has a probability of Q(T) of defaulting by time T the default rate that will not be exceeded at the X% confidence level is ⚫ Where r is the Gaussian copula correlation −r + r − − 1 ( ) ( ) 1 1 N Q T N X N 7
VaR Model (Equation18.2,page 402)Z WCDR,(T,X)×EAD, ×LGD,VaR=RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull20128
VaR Model (Equation 18.2, page 402) Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 8 = i i T X EADi LGDi VaR WCDR ( , )
Credit Risk Plus (Section 18.3, page 403)This calculates a loss probability distribution using aMonte Carlo simulation where the steps are:Sample overall default rateSample probability of default for each counterpartycategorySample number of losses for each counterparty categorySample size of loss for each defaultCalculate total loss from defaultsThis is repeated many times to calculate a probabilitydistribution for the total lossRiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull20129
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 Credit Risk Plus (Section 18.3, page 403) This calculates a loss probability distribution using a Monte Carlo simulation where the steps are: ⚫ Sample overall default rate ⚫ Sample probability of default for each counterparty category ⚫ Sample number of losses for each counterparty category ⚫ Sample size of loss for each default ⚫ Calculate total loss from defaults This is repeated many times to calculate a probability distribution for the total loss 9
CreditMetrics (Section 18.4, page 405). Calculates credit VaR by consideringpossible rating transitionsA Gaussian copula modelis used to definethe correlation between the ratingstransitions of different companies10RiskManagementandFinancialInstitutions3e,Chapter18,CopyrightJohnC.Hull2012
Risk Management and Financial Institutions 3e, Chapter 18, Copyright © John C. Hull 2012 CreditMetrics (Section 18.4, page 405) ⚫ Calculates credit VaR by considering possible rating transitions ⚫ A Gaussian copula model is used to define the correlation between the ratings transitions of different companies 10