It is the cross-default clauses in debt agreements that generally provide that a default on one obligation is considered a credit event applying to all debts of the obligor, and therefore we are able to deal with credit risk at the borrower level, and not at the level of the individual security. It also helps avoid situations where borrowers can selectively default on some obligations while continuing to service others. Therefore Choice ' a ' is the correct answer. The other choices are incorrect.

Choice ' c ' correctly describes Altman ' s z-score. All other choices are incorrect.

First of all, if prices are lognormally distributed, that implies the returns (which are equal to the log of prices) are normally distributed. To say that prices are lognormally distributed is just another way of saying that returns are normally distributed.

Since the correlation between the two securities is zero, this means their variances can be added. But standard deviations, or volatilities cannot be added (they will be the square root of sum of variances). VaR is nothing but a multiple of standard deviation, and therefore it is not additive if correlations are anything other than 1 (ie perfect positive, which would imply we are dealing with the same asset). Therefore VaR(A+B)=SQRT(VaR(A)^2 + VaR(B)^2). This implies the combined VaR of a portfolio with these two securities will be less than the sum of VaRs of the two individual securities.

Thus Choice ' c ' is the correct answer and the other choices are wrong.

Regardless of the approach being followed by a bank (ie, whether foundation IRB or advanced IRB), it must make its own estimates for the probability of default. Banks following the foundation IRB approach may use values set by the supervisor for the other three parameters, though those following the advanced IRB approach may use their own estimates for all four inputs. (This is also the difference between advanced IRB and the foundation IRB approaches.) Therefore Choice ' a ' is the correct answer.

Also note the four difference elements that go as inputs to the internal ratings based approach in the choices provided.

The correct definition of CVA is LGD * EPE * PD. All other answers are incorrect.

CVA reflects the adjustment for counterparty default on derivative and other trading book transactions. This reflects the credit charge, that neeeds to be reduced from the expected value of the transaction to determine its true value. It is calculated as a product of the loss given default, the probability of default and the average weighted exposure of future EPEs across the time horizon for the transaction.

The future exposures need to be discounted to the present, and occasionally the equations for CVA will state that explicitly. Similarly, in some more advanced dynamic models the correlation between EPE and PD is also accounted for. The conceptual ideal though remains the same: CVA=LGD*EPE*PD.

The correct answer is Choice ' b ' . The following is a brief description of the major approaches available to model credit risk, and the analysis that underlies them:

1. CreditMetrics: based on the credit migration framework. Considers the probability of migration to other credit ratings and the impact of such migrations on portfolio value.

2. CreditPortfolio View: similar to CreditMetrics, but adds the impact of the business cycle to the evaluation.

3. The contingent claims approach: uses option theory by considering a debt as a put option on the assets of the firm.

4. KMV ' s EDF (expected default frequency) based approach: relies on EDFs and distance to default as a measure of credit risk.

5. CreditRisk+: Also called the ' actuarial approach ' , considers default as a binary event that either happens or does not happen. This approach does not consider the loss of value from deterioration in credit quality (unless the deterioration implies default).

Model risk is the risk that a model built for estimating a variable will produce erroneous estimates. Model risk is caused by a number of factors, including:

a) Misspecifying the model: For example, using a normal distribution when it is not justified.

b) Model misuse: For example, using a model built to estimate bond prices to estimate equity prices

c) Parameter estimation errors: In particular, parameters that are subjectively determined can be subject to significant parameter estimation errors

d) Programming errors: Errors in coding the model as part of computer implementation may not be detected by end users

e) Data errors: Errors in data used for building the model may also introduce model risk

Therefore the correct answer is d, as all the choices are a source of model risk.

Explanation

If the risks are considered perfectly positively correlated, ie assumed to have a correlation equal to 1, the standard deviations can simply be added together. This gives the most conservative estimate of combined risk for capital calculation purposes. In practice, this is the assumption used most often.

If risks are uncorrelated, ie correlation is assumed to be zero, variances can be added or the standard deviation is the root of the sum of the squares of the individual standard deviations. This obviously gives a number lower than that given when correlation is assumed to be +1.

Similarly, assumptions of negative correlation, or any correlation other than +1 will give a standard deviation number that is smaller and therefore less conservative. Choice ' b ' is the correct answer.

Error rates are generally modeled using the Poisson distribution. Recall that the Poisson distribution has only one parameter - λ - which is its mean and also its variance.

In the given case, the mean number of errors is 2,000,000 x 0.005% = 100. Since this is the variance as well, the standard deviation is √100 = 10. Therefore the range of outcomes within 2 standard deviations of the mean is 100 +/- (2*10) = 80 to 120 errors in a day.

When calculating volatility weighted VaR, returns are adjusted by a factor equal to the current volatility divided by the historical volatility, ie the volatility that existed during the time period the returns were earned. If the current volatility is greater than the historical volatility (also called contemporary volatility), then it has the effect of increasing the magnitude of any past returns (whether positive or negative). This in turn increases the VaR.

Consider an example: if the current volatility is 2%, and a return of -5% was earned at a time when the volatility was 0.8%, then the volatility weighted return would be 12.5% (=-5% x 2%/0.8%). Clearly, this has the effect of increasing the VaR.

Choice ' d ' is therefore the correct answer.