8008 Exam Dumps : PRM Certification - Exam III: Risk Management Frameworks, Operational Risk, Credit Risk, Counterparty Risk, Market Risk, ALM, FTP - 2015 Edition

GARCH is a mean reverting model of volatility, with a steady state mean that the model reverts to in the absence of market shocks. EWMA is not mean reverting and volatility under EWMA stays constant in the absence of shocks. Therefore statement I is correct.

Both EWMA and GARCH models are designed to address volatility clustering, which explains much of the non-normality of returns. When returns are standardized to the volatility calculations under either of these methods, the returns appear far closer to the normal distribution than non-standardized returns. (If it were not to, then there would have been no point in using these techniques.) Statement II is correct.

Steady state variance under GARCH is defined as ω / (1 - α - β), where α and β are the two parameters (called the reaction and persistence coefficient respectively). Clearly, it is affected by more than just the persistence coefficient, therefore statement III is not correct.

Sub-additivity is a very desired property in risk measures. It implies the sum of the parts is greater than the whole. In the case of risk measures, the whole is smaller than the sum of the parts due to diversification. Statement IV is true.

Therefore the correct answer is Choice 'c'

A default hazard rate is the rate of default in a continuous time setting. This question is asking for probability of survival at the end of 5 years. The formula to calculate the probability of survival at the end of t years where the default hazard rate is λ is e^(-λ *t) (or in Excel, =exp(-λ*t). Therefore the correct answer is Choice 'd'.

(It may be tempting to infer that if the probability of survival at the end of 1 year is 90% (1 - 10%), then the probability of survival in 5 years would be 90%^5. However this reasoning is not correct for the reason that the given rate is not the discrete rate of default, but the hazard rate which is nothing but the continuously compounded rate of default.)

For operational risk modeling, both frequency and severity distributions need to be modeled. Modeling severity involves finding an analytical distribution, such as log-normal or other that approximates the distribution best represented by known data - whether from the internal loss database, the external loss database or scenario data. A 'risk functional' is a measure of the deviation of the model distribution from the risk's actual severity distribution. It assigns a penalty value for the deviation, using a statistical measure, such as the KS distance (Kolmogorov-Smirnov distance).

The problem of finding the right distribution then becomes the problem of optimizing the risk functional. For example, if F is the model distribution, and G is the actual, or empirical severity distribution, and we are using the KS test, then the Risk Functional R is defined as follows:

Note that supx stands for 'supremum', which is a more technical way of saying 'maximum'. In other words, we are calculating the maximum absolute KS distance between the two distributions. (Note that the KS distance is the max of the distance between identical percentiles of the two distributions using the CDFs of the two.)

Once the risk functional is identified, we can minimize it to determine the best fitting distribution for severity.