Pass the PRMIA PRM 8008 Questions and answers with ValidTests

The bank will not be able to recover the principal advanced on this loan if both the home buyer defaults, and the house value falls to less than $1m, ie the price moves adversely by more than $500k, which is $-500k/$150k = -3.33σ. (Note that 150k is the 1 year volatility in dollars, ie $1.5m * 10%).

The probability of both these things happening together is just the product of the two probabilities, one of which we know to be 5%. The other is also certainly a small number, and intuitively it is clear that the probability of both the things happening together will be less than 1%.

For a more precise answer, we can calculate the probability of the house price falling by 3.33 standard deviations by calculating the area under the standard normal curve to the left of -3.33σ. This indeed is a very small number (actually equal to NORMSINV(-3.33)=0.00043), which when multiplied by the probability of default of the home buyer at 5% is certainly going to be less than 1%. Therefore Choice 'b' is the correct answer.

If returns display mean reversion, then clearly daily volatilities will be greater than weekly volatility, both annualized using the square root of time rule. Mean reversion would imply that the deviation from the mean will be lower over a longer time period than a shorter time period, and therefore annualized volatility based on daily volatility will be greater.

Hazard rate x Loss given default = CDS quote. In other words, Hazard rate x (1 - recovery rate) = CDS quote. We can therefore calculate the hazard rate for this problem as 200 bps/(1 - 40%) = 3.33%.

The persistence parameter, β, is the coefficient of the most recent day's returns in GARCH calculations. A higher value of the persistence parameter tends to 'persist' the prior value of variance for longer. Consider an extreme example - if the persistence parameter is equal to 1, the variance under GARCH will never change in response to returns.

The minimum multiplication factor specified under Basel II is 3. Therefore the correct answer is Choice 'a'. The exact requirements are laid down below.

Each bank must meet, on a daily basis, a capital requirement expressed as the higher of (i) its previous day’s value-at-risk number measured according to the parameters specified in this section and (ii) an average of the daily value-at-risk measures on each of the preceding sixty business days, multiplied by a multiplication factor.

The multiplication factor will be set by individual supervisory authorities on the basis of their assessment of the quality of the bank’s risk management system, subject to an absolute minimum of 3. Banks will be required to add to this factor a “plus” directly related to the ex-post performance of the model, thereby introducing a built in positive incentive to maintain the predictive quality of the model. The plus will range from 0 to 1 based on the outcome of so-called “backtesting.”

There are multiple ways to incorporate scenario analysis for modeling operational risk capital - and the exact approach used depends upon the quantity of loss data available, and the quality of scenario assessments. Generally:

- If there is no past loss data available, scenarios are the only practical means to model operational risk loss distributions. Both frequency and severity estimates can be modeled based on scenario data.

- If there is plenty of past data available, scenarios can be used as a modifier for estimates that are based solely on data (for example, consider the MAX of the loss estimates at the desired quantile as provided by the data, and as indicated by scenarios)

- If high quality scenario data is available, and there is sufficient past data, one could mix scenario assessments with the loss data and fit the combined data set to create the loss distribution. Alternatively, both could be fitted with severity estimates and then the two severities could be parametrically combined.

In short, there is considerable flexibility in how scenarios can be used.

Statement I is therefore correct, and so is statement II as both indicate valid uses of scenarios.

Statement III is not correct because it may be okay to create severity estimates based on scenario data alone.

Statement IV is not correct because while using scenarios as modifiers to other means of estimation is acceptable, that is not the only use of scenarios.

According to ISDA standard definitions, the legal claim for OTC derivatives is the current replacement value of the contract. Therefore Choice 'c' is the correct answer. None of the other choices are correct.

One way to think about this question is this: we are provided with two pieces of information: if the portfolio is worth $100 to start with, it will be worth $95 at the end of year 1 and $85 at the end of year 2. What it is asking for is the probability of default in year 2, for the debts that have survived year 1. This probability is $10/$95 = 10.53%. Choice 'b' is the correct answer.

Note that marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2... n are p1, p2...pn, then cumulative probability of default can be calculated as Cn = 1 - (1 - p1)(1-p2)...(1-pn). For this question, we can calculate the probability of default for year 2 as [1 - (1 - 5%)(1 - 10.53%)] = 15%.

According to the first principle set out by the BCBS paper on stress testing, the Board has ultimate responsibility for the overall stress testing programme. Senior management is accountable for the implementation, management and oversight of the programme, but the overall responsibility stays with the Board of Directors of the institution. Therefore Choice 'c' is the correct answer.

Additionally, this principle lays down that stress testing should be a part of the overall governance, ie support the strategic choices made as part of business planning; and be integrated with the risk management culture of the bank, ie stress tests should be used as an input for setting the risk appetite, exposure limits, and the capital and liquidity planning processes of the bank.

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.