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

1. A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points

A) 10 basis point rise
B) 30 basis points fall.
C) 24 basis point rise
D) 24 basis fall

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

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

3. Consider the following distribution data for a random variable X: What is the mean and variance of X?

A) None of these
B) 3.4 and 3.84
C) 3.5 and 3.45
D) 3.6 and 7.15

4. A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?

A) 7.44
B) 6.59
C) 7.12
D) 7.29

5. Which statement regarding the matrix below is true?

A) It is positive definite
B) It is negative definite
C) It is positive semi-definite
D) It is not positive definite

Solutions: