8008 PRMIA Exam Lab Questions

Stress testing is used for all the listed purposes. Therefore Choice 'a' is the correct answer.

When a derivative transaction is entered into, its value generally is close to zero. Over time, as the value of the underlying changes, the transaction acquires a positive or negative value. It is not possible to predict the future value of the transaction in advance, however distributional assumptions can be made and potential exposure can be measured in multiple ways. Of all the possible future exposures, it is generally positive exposures that are relevant to credit risk because that is the only situation where the bank may lose money from a default of the counterparty.

The maximum (generally a quantile eg, the 97.5th quantile) exposure possible over the time of the transaction is the 'Potential Future Exposure', or PFE.

The average of the distribution of positive exposures at a specified date before the longest trade in the portfolio is called 'Expected Exposure', or EE.

The expected positive exposure calculated as the weighted average of the future positive Expected Exposure across a time horize is called the EPE, or the 'Expected Positive Exposure'.

The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date - is the 'fair value', as defined under FAS 157.

Therefore the corect answer is that EPE is the weighted average of the future positive expected exposure across a time horizon.

The actuarial or CreditRisk+ model considers default as an 'end of game' event modeled by a Poisson distribution. The annual number of defaults is a stochastic variable with a mean of μ and standard deviation equal to √μ.

The probability of n defaults is given by (μ^n e^-μ) /n!, and therefore in this case is equal to (=2^4 * exp(-2))/FACT(4)) = 0.0902.

Note that CreditRisk+ is the same methodology as the actuarial approach, and requires using the Poisson distribution.

In the univariate Gaussian model, each risk factor is modeled separately independent of the others, and the dependence between the risk factors is captured by the covariance matrix (or its equivalent combination of the correlation matrix and the variance matrix). Risk factors could include interest rates of different tenors, different equity market levels etc.

While this is a simple enough model, it has a number of limitations.

First, it fails to fit to the empirical distributions of risk factors, notably their fat tails and skewness. Second, a single covariance matrix is insufficient to describe the fine codependence structure among risk factors as non-linear dependencies or tail correlations are not captured. Third, determining the covariance matrix becomes an extremely difficult task as the number of risk factors increases. The number of covariances increases by the square of the number of variables.

But an inability to capture linear relationships between the factors is not one of the limitations of the univariate Gaussian approach - in fact it is able to do that quite nicely with covariances.

A way to address these limitations is to consider joint distributions of the risk factors that capture the dynamic relationships between the risk factors, and that correlation is not a static number across an entire range of outcomes, but the risk factors can behave differently with each other at different intersection points.