Foundations of Credit Risk Modelling von Edu Pristine

Dozent des Vortrages Foundations of Credit Risk Modelling

Edu Pristine

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... This section maybe read independent of any other section. However, knowledge of Probability distributions, especially Normal, Beta & Poisson distribution (Refer part: Mathematical Foundations) & Portfolio Variance is preferable. This reading material would help you find answer to the following questions: A bank is lending to borrowers with different credit rating and different expected recoveries, if they default. How should it price these exposures? What is the maximum loss possible on a portfolio of many credit exposures i.e. Credit VaR? ...

... a sovereign might put moratorium on payment of foreign currency debt for some time because of shortage of foreign currency reserves. Insolvency: Inability to pay. Bankruptcy: Start of legal procedure by creditors to ensu re fair treatment of all creditors by the shareholders. Default: Failure to meet any obligation, including n on covenants. Most of the material that follows relates to credit def ault risk. It will be easy to understand most of the concepts if you put yourself in a banker’s shoes. Payment on due date because of: Credit default: payment default on borrowed money (loans , bonds, Line of credit). ...

... The Bank estimates that if the borrower defaults in the next one year, he is likely to utilize 80% of the present unutilized limits (it is logical to assume that prior to default, a person/ firm is likely to utilize maximum of the available limits). In this case, EAD = 40 + 60* 80% = $ 88. Remember, EAD is an ‘estimate’. Prior to management of credit risk, it is imperative to measure credit risk. At individual exposure level (say, credit risk in loans given to ABC Ltd.). At portfolio level (say, credit risk in loans given to real estate sector). Credit risk is measured for a specific time horizon (1 year in most cases) Following parameters are required to measure credit risk at individual exposure (loan, bond etc.): = Current outstanding + Undrawn limit * x%. For instance, a bank has sanctioned a loan of $ 100 to a customer... ...

... The borrower has EL of a portfolio = Sum of EL of all assets in the portfolio (We know from portfolio theory, expected return on a portfolio is simply the sum of expected returns on individual asset in the portfolio because 1.20% 1.20 $ 2% 40%)-==× A bank has made the following three loans: Loan1 of Rs.100 crores to AAA rated borrower with PD o f 0.03%, LGD of 20% i.e. EL = Crores -Loan2 of Rs.100 crores to BBB rated borrower with PD of 1%, LGD of 50% i.e. EL Crores -Loan3 of Rs.100 crores to BB rated borrower with PD of 7% ...

... In the previous example, assume the Bank lends 100 loans o f Rs.100 each to BB7 rated borrowers at 11.60% (PD of 7%, LGD of 80%). Total portfolio size = 6.006% 6.50% 11.60% 10,000 100 100=×, Pristine10 EL (Cont+) For any single borrower, there are only two possibilities: Default: In that case, bank would lose Rs.80 (LGD*EAD) for each defaulting borrower. No default: Bank’s loss would be zero. At the portfolio level, we would expect 7 borrowers to default (PD of 7%) (in reality, number of losses may be higher or lesser than the average number of 7 loses expected, say depending on performance of the economy). The Bank loss would be risk premium (called credit spread) being charged from each borrower. ...

... Credit VaR is the 99.xx percentile (actual percentile would depend on the desired credit rating of the Bank, or as specified by the regulator) of the loss distribution EL% = PD*LGD, EL in Rs. ...

... EAD also assumes a certain utilization level of unutilized limits. Actual utilization level may be higher or lesser than expected, leading to randomness of EAD parameter. If we know with certainty that in a portfolio of 100 loans, exactly 7 would default (no less, no more), then actual loss would be equal to EL and UL would be zero. However, life is not that simple (as shown by current credit crisis, where actual mortgage loans default far exceeded EL and even One would always see years of great, average, poor economic/ industrial/ corporate performance; leading to actual No. of losses being higher than or lesser than expected number of losses. This brings randomness to ‘No. of defaults’ parameter (captured by PD). Similarly, if we expect LGD of 60% on a loan, then actual loss might be higher or lesser than this estimate because of various factors (sharp decline in proper ty prices leading to lower recoveries, legal problems). This bring randomness to ‘Expected recoveries’ parameter (captured by LGD = 17 EAD also assumes a certain utilization level of unutilized limits. Actual utilization level may be higher or lesser than expected, leading to randomness of EAD parameter. Pristine14 Unexpected loss (Cont+). ...

... When borrowers show high positive default correlation (say, for a highly concentrated portfolio to real estate sector), portfolio UL is high. With low default correlation (say, a well diversified portfolio across various sectors), portfolio UL is low. Negative default correlation is rare, but portfolio UL would be minimum with negative default correlation between borrowers. – ‘r’ is the default correlation between borrower ‘A’ and ‘B’. ) We may simply note that EL is mean of likely loss distributi on, UL is standard deviation of likely loss (the equation assumes EAD and LGD are constant. ...

... Usually, the confidence interval should be in line with desired credit rating of the bank. For instance, a bank desiring to be AA rated should calculate credit VaR for its portfolio at 99.97% (AA rated banks have less than 0.03% PD) and then subtract EL, to compute capital requirement for UL. Unexpected loss (Cont+) denotes the level of Unexpected loss for which capital is required. This ensures that a bank has sufficient capital to cover portfolio losses in 99.9% cases (EL is subtracted because it is assumed that bank would have already recovered this loss level through correct.

... R and Economic capital requirement is dependant on PD, LGD, EAD and default correlation, the other PPTs are related to estimation of: – PD – LGD – EAD.

... The recovery rate is the value of the default settlement per unit of legal claim, discounted back to the date of default and after subtracting legal and administrative costs. The factors that affect the recovery rates are – Collateral – Legal priority of the class of the claim – The country in which the default event takes place. The recovery rate (or the LGD) is important in determining default losses or expected default losses. However, the data on recovery rate is very unreliable than that of default events. ...

... Beta Distribution for Predicting Recovery Rates Beta distribution has been popularly used in predicting recovery rates. The probability distribution , where and c is a normalization constant. ...