【正文】 b a b a i l i t yR a t i n g R a t e V a l ue ( % )AAA R f + S AAA 110 0. 02AA R f + S AA 109 0. 33A R f + S A 108 5. 95BBB R f + S BBB 107 86. 93BB R f + S BB 102 5. 3B R f + S B 98 1. 17CCC R f + S CCC 84 0. 12D e f a ul t 1 R R 51 0. 18Now, the loan is rated BBB. Its bond equivalent yield is Rf + SBBB. 1 year Bank of Thailand 34 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics 02040608010060 80 100 120L o a n v a l u eP rob a bi l i t y (%)Loss = Vcurrent Vnew EL, UL, Percentile, and VaR can be found. E(V) V(1st percentile) VaR Bank of Thailand 35 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics In the portfolio level, correlations are needed to bine all counterparties (or loans) and find the portfolio loss distribution: “Ability to pay” = “Normalized equity value” Migration probabilities predefine buckets (lower and upper thresholds) for the future ability to pay Correlation of default and migrations can, hence, be derived from correlation of the “ability to pay”. Bank of Thailand 36 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics In order to find the loss distribution of a 2counterparty portfolio, we need to calculate the joint migration probabilities and the payoffs for each possible scenario: ? ??????BBZBZAZBBBZABBBBBB drdrrrfZrZZrZP 212121 )。,(),( ?Probability that counterparty 1 and 2 will be rated BB and BBB respectively Bank of Thailand 37 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics AAA AA A BBB BB B CCC De faul t AAA AA A BBB BB B CCC De faul t Obligor2 ( A)Obligor1(BBB )Sample Joint Transition Matrix(assuming asset correlation) Source: Credit Metrics Technical Document, April 2, 1997, p. 38 Bank of Thailand 38 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics For N counterparties, one way to find the loss distribution is to keep expanding the joint transition matrix. This, however, rapidly bees putationally difficult (the number of possible joint transition probabilities is 8N). Another way is to sum counterparty asset volatilities is to use the variance summation equation. This is acceptable only for the loss distributions that are close to normal. Bank of Thailand 39 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics For puting the distribution of loan values in the large sample case where loan values are not normally distributed, Credit Metrics uses Monte Carlo simulation. The Credit Metrics portfolio methodology can also be used for calculating the marginal risk contribution (RC) for individual counterparties. RC is useful in identifying the counterparties to which we have excessive risk exposure. Bank of Thailand 40 Risk Management Symposium September 2023 Credit Risk Models (D) Credit Metrics Exposure Distribution Rating migration likelihoods Spread matrix and recovery rates Correlations Joint credit rating changes Portfolio ponents and market volatilities Value and loss distribution of individual obligors Portfolio value and loss distribution EL, UL, Percentile, and VaR can be found. Summary Bank of Thailand 41 Risk Management Symposium September 2023 Credit Risk Models (E) “KMVType” Model One or both defaults and spread changes due to rating upgrades/downgrades can be incorporated. EDF is firmspecific. EDF varies continuously with firm asset value and volatility. Potentially a continuous credit migration. Bank of Thailand 42 Risk Management Symposium September 2023 Credit Risk Models (E) “KMVType” Model Analysis is done on each individual counterparty, which will then be bined into a portfolio, using assetvalue correlations. Therefore, the only key type of uncertainty modeled here is whether or not the asset value of each firm, one year from now, will be higher than the value of its liabilities. Bank of Thailand 43 Risk Management Symposium September 2023 Credit Risk Models (E) “KMVType” Model Ability to pay = Asset value Time 0 1 Default point = Value of liabilities Asset value distribution Default probability Value Bank of Thailand 44 Risk Management Symposium September 2023 Credit Risk Models (E) “KMVType” Model The question is “how to find the distribution of future asset value”. KMV defines the distribution by the mean asset value and the asset volatility (or standard deviation). The question now bees “how to find the asset value and its volatility”. Bank of Thailand 45 Risk Management Symposium September 2023 Credit Risk Models (E) “KMVType” Model Since we can observe only equity value and its volatility, the link between equity and asset values and that between equity and asset volatilities need to be established. KMV solve this problem using an option pricing model. Bank of Thailand 46 Risk Management Symposium September 2023 Credit Risk Models (E) “KMVType” Model 0 Firm value Liability value 0 Firm value Equity value Book value of liabilities Book value of liabilities Liabilities ~ “Short put” Equity ~ “Long call” Bank of Thailand 47 Risk M