PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition : 8007

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

1. A 95% confidence interval for a parameter estimate can be interpreted as follows:

A) The probability that the estimated value of the parameter is within this interval is 95%.
B) The probability that the real value of the parameter is outside this interval is 95%.
C) The probability that the real value of the parameter is within this interval is 95%.
D) The probability that the estimated value of the parameter is outside this interval is 95%.

2. A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?

A) 0.96
B) 1.92
C) 0.32
D) 0.64

3. Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

A) 0.5
B) 2
C) 1
D) 0

4. 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) 17.33
B) 20.54
C) 18.75
D) 19.23

5. You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

A) b=2, a=0
B) b=0.5, a=1.5
C) b=2, a=4
D) b=0.5, a=2.5

Solutions: