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

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

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

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

2. In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

A) 0.5290
B) 0.5286
C) 0.5292
D) 0.5288

3. In a multiple linear regression, the significance of R2 can be tested using which distribution?

A) Normal distribution
B) Student's t distribution
C) Binomial distribution
D) F-distribution

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) 6.59
B) 7.44
C) 7.29
D) 7.12

5. An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101.
Approximate the value of the option delta using a first order central finite difference.

A) -0.25
B) 0.25
C) -0.5
D) -4

Solutions: