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

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.

The recovery rate, the default hazard rate (also called the average default intensity) and the spread on debt are linked by the equation Hazard Rate = Spread/(1 - Recovery Rate). Therefore, the recovery rate implicit in the given data is = 1 - 8%/10% = 20%.

Historical Simulation VaR is conceptually very straightforward: actual prices as seen during the observation period (1 year, 2 years, or other) become the 'scenarios' forming the basis of the valuation of the portfolio. For each scenario, full revaluation is performed, and a P&L data set becomes available from which the desired loss quantile can be extracted.

Historical simulation is based upon actually seen prices over a selected historical period, therefore no distributional assumptions are required. The data is what the data is, and is the distribution. Statement I is therefore not correct.

It uses full revaluation for each historical scenario, therefore statement II is correct.

Since the prices are taken from actual historical observations, a correlation matrix is not required at all. Statement III is therefore incorrect (it would be true for Monte Carlo and parametric Var).

Historical simulation VaR suffers from the limitation that if enough representative data points are no available during the historical observation period from which the scenarios are drawn, the results would be inaccurate. This is likely to be the case for new products. Therefore Statement IV is incorrect.