PRMIA PRM 8007

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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

A) flat and thick at the center and with thin tails
B) peaked and thin at the center and with heavy (fat) tails
C) peaked and thin at the center and with thin tails
D) flat and thick at the center and with heavy (fat) tails

2. An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?

A) 0.02
B) 0.14
C) 0.25
D) 0.50

3. An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European call option has a strike of 85 and a maturity of 40 days. Its Black-Scholes price is 15.52. The options sensitivities are: delta = 0.98; gamma = 0.006 and vega = 1.55. What is the delta-gamma-vega approximation to the new option price when the underlying asset price changes to 105 and the volatility changes to 28%?

A) 20.54
B) 17.33
C) 19.23
D) 18.75

4. Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A) arithmetic sequence, common difference 2
B) arithmetic sequence, common ratio 2
C) geometric sequence, common ratio 3
D) geometric sequence, common ratio 2

5. Which of the following statements about variance and standard deviation are correct?
1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation
2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data
3. When considering independent variables, variance is additive, while standard deviation is not

A) Statements 2 and 3 are correct
B) Statements 1 and 3 are correct
C) All three statements are correct
D) Statements 1 and 2 are correct

Solutions: