1 An Integrative Approach to Managing Credit Risks Based on Crouhy, Galai, Mark, Risk Management, McGraw- hill,2000, (ch. 9)

2 Theory of Risk Measurement

3 Typology of Risk Exposure (partical list) Market Risk is the risk that changes in financial markets prices and rates will impact the value of the banks positions.  Interest Rate Risk  Stock Market Risk  FX Risk  Commodity Risk  Inflation Risk Credit Risk is the risk that changes in the credit quality of the counterparty affects the value of the bank’s position. Default Risk is the extreme case where the counterparty is unwilling or unable to fulfill its contractual obligation. Downgrading Risk is the risk that a counter party credit quality declines. Liquidity Risk is the risk of not being able to execute a transaction at the current prevailing market price. Operational Risks is the risk for potential losses resulting from inadequate systems, faulty contracts, frauds, human errors, failure of technology

4 Schematic presentation, by categories, of the risk exposure of a bank Bank’s Risks Operational Risk Credit Risk Portfolio concentration risk Transaction Risk Infrastructural Risk Process Risk Market Risk Equity Risk Interest Rate Risk Currency Risk Commodity Risk Model Risk Gap Risk Trading Risk Issuer Risk Counterparty Risk Liquidity Risk Regulatory Risk Human Factor Risk

5 Market Risk Business risk of firm i Default risk of debt of firm i Interest Rate Risk Commodity Risk Foreign Exchange Risk Equity Risk Real Estate Risk Financial risk of equity of firm i

6

7 Where (1)(CAPM) (2)(CAPM) (3)(MM)

8 (4)(OPM) (5)(OPM) (6)(OPM & CAPM) (7)(OPM & CAPM)

Credit Risk Revisited: An Option Pricing Approach

10 Bank’s pay-off matrix at time 0 and T for making a loan and buying a put

11 (2) where P is the current value of the put, N(.) is the cumulative standard normal distribution, and and  is the standard deviation of the rate of return of the firm’s assets.

12 We can now derive the yield to maturity for the corporate discount debt,, as follows: so that the default spread,, defined as, can be derived from (2): (3)

13 Default spread of corporate debt (For V 0 =100,T=1, and r-10% 5 )

14 Default Premium (DP): DP = (RB - RV)*Probability of default where RV = recovery value RB = value of the riskless bond

15 Using the same numerical example as in the previous section (i.e. V 0 =100, T=1, r=10%,  =40%, F=77 and LR=0.7), we obtain: Discounted expected recovery value Value of Riskless Bond=77.e = 70 Expected Shortfall= = 13.9 Probability of Default=24.4% Cost of Default 7 = = 3.39

16 EL T =probability of default x loss in case of default = N(-d 2 )F-N(-d 1 )Ve rT (5) EL T = e =

17 In a continuous time framework it can be shown that credit risk has a systematic risk related to market risk, as follows:

18 and the capital charge, CC SR for specific risk for the zero-coupon bond, is: 1 In our example, assuming  m =20%, we find SR= and CC SR = The capital charge corresponds to a maximum loss at the one-tailed 99% confidence interval over a 10 day horizon. Assuming normality of the price change variations, and serial independence, the instantaneous volatility needs to be scaled up by the factor. There is an additional multiplier of 3 required by BIS to compensate for additional risks not captured by the model, like liquidity risk.