【正文】 can be viewed as a uniform portfolio. m counterparties a uniform default probability of p(m) Bank of Thailand 18 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) DP Counterparties m1, p(m1) m2, p(m2) m3, p(m3) m4, p(m4) Bank of Thailand 19 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) Within each class of counterparties, number of defaults follows Poisson Distribution. !)(nenP n????mmp *)(??m = number of counterparties p(m) = uniform default probability n = number of defaults in 1 year Bank of Thailand 20 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) If default intensity ( ) is constant, defaults are implicitly assumed to be independent (zero correlation). This is the old approach. We know that counterparties are somewhat dependent. As a result, the old approach is not realistic (too optimistic). ?Bank of Thailand 21 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) The new approach incorporates dependency of counterparties by assuming that default intensity is random and follows gamma distribution. ),(~ ??? ? defines shape, and defines scale of the distribution. ??Default intensity Probability density Bank of Thailand 22 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) Number of defaults (n) Default intensity ( ) ? ),(~ ??? )(~ ?Poissonn ),(~ ???nomialNeg ativeBinBank of Thailand 23 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) Defaults are now related since they are exposed to the same default intensity. Higher default intensity effects all obligors in the portfolio. First moment: Second moment: ???)(nE )1()( ??? ??nVMean Variance (Overdispersion) Bank of Thailand 24 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) Negative Binomial Distribution (NGD) exhibits overdispersion and “fatter tails”, which make it closer to reality than Poisson Distribution. of defaults Probability density Poisson Negative Binomial EL(P) = EL(NGD) UL(P) UL(NGD) Bank of Thailand 25 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) The last source of uncertainty is the loss amount in case of default (LEE*LGD) This is modeled by bucketing into exposure bands and identifying the probability that a defaulted obligor has a loss in a given band with the percentage of all counterparties within this given band. Bank of Thailand 26 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) 0%10%20%30%40%50%U n d e r 5 0 5 0 t o 1 0 0 1 0 0 t o 2 0 0 O v e r 2 0 0Lo s s am ou ntP r ob ab i l i t yProbability Distribution of Loss Amount Bank of Thailand 27 Risk Management Symposium September 2023 Credit Risk Models (C) Model from Insurance (Credit Risk+) Probability distribution of of defaults 0%10%20%30%40%50%U n d e r 5 0 5 0 t o 1 0 0 1 0 0 t o 2 0 0 O v e r 2 0 0Lo s s am ou ntP r ob ab ilityProbability distribution of loss amount The analytic formula of the loss distribution in the form of probability generating function (PGF) Probability, EL, UL, and Percentile can be found. Bank of Thailand 28 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics Introduced in 1997 by . Man. Both defaults and spread changes due to rating upgrades/downgrades are incorporated. Credit migration (including default) is discrete. All counterparties with the same credit rating have the same probability of rating upgrades, rating downgrades, and defaults. Bank of Thailand 29 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics Analysis is done on each individual counterparty, which will then be bined into a portfolio, using correlations. Therefore, the only key type of uncertainty modeled here is the credit rating (or default) at which a particular counterparty will be one year from now. Bank of Thailand 30 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics Rating Time 0 1 BBB BBB AAA B Default Bank of Thailand 31 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics In the counterparty level, two inputs are required: 1. Credit transition matrix (Moody’s, SP or KMV) I n i t i a lR a t i n g AAA AA A BBB BB B CCC DAAA 90. 81 8. 33 0. 68 0. 06 0. 12 0 0 0AA 0. 7 90. 65 7. 79 0. 64 0. 06 0. 14 0. 02 0A 0. 09 2. 27 91. 05 5. 52 0. 74 0. 26 0. 01 0. 06BBB 0. 02 0. 33 5. 95 86. 93 5. 3 1. 17 0. 12 0. 18BB 0. 03 0. 14 0. 67 7. 73 80. 53 8. 84 1 1. 06B 0 0. 11 0. 24 0. 43 6. 48 83. 64 4. 07 5. 2CCC 0. 22 0 0. 22 1. 3 2. 38 11. 24 64. 86 19. 79R a t i n g a t Y e a r E n d ( % )Source: Standard Poor’s CreditWeek April 15, 1996 Bank of Thailand 32 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics 2. Spread matrix and recovery rates Source: Carty Lieberman (96a) Moody’s Investor Service C r edi t C