8010 Exam Dumps : Operational Risk Manager (ORM) Exam

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 3 as =1 - (1-2%)*(1-3%)*(1-4%) = 8.74%

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 revaluationis 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. Thedata 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 correlationmatrix 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.

If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of both of them defaulting together is affected by the default correlation between them. Marginal probability of default means the probability of default of each security on a standalone basis, ie, the probability of default of one security without considering the other security.

The relationship that expresses the probability of joint default of the two is given by the following expression:

It is easy to see that in a situation where the Default Correlation of A & B = 0, ie, the defaults are independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p, ie the securities behave in an identical way, the expression resolves to just p, which is what we would expect.

From the above relationship, it is clear that the probability of joint default of A and B is the greatest when default correlation between the two is equal to 1, ie the securities behave in an identical way. Therefore Choice 'a' is the correct answer.