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

1. In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

A) 6.31
B) 4.18
C) 5.19
D) 5.66

2. Your stockbroker randomly recommends stocks to his clients from a tip sheet he is given each day. Today, his tip sheet has 3 common stocks and 5 preferred stocks from Asian companies and 3 common stocks and 5 preferred stocks from European companies. What is the probability that he will recommend a common stock AND/OR a European stock to you when you call and ask for one stock to buy today?

A) 7/8
B) None of these
C) 9/16
D) 11/16

3. Which of the following can induce a 'multicollinearity' problem in a regression model?

A) A high positive correlation between two explanatory variables
B) A high positive correlation between the dependent variable and one of the explanatory variables
C) A large negative correlation between the dependent variable and one of the explanatory variables
D) The omission of a relevant explanatory variable

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

5. A 2-year bond has a yield of 5% and an annual coupon of 5%. What is the Macaulay Duration of the bond?

A) 1.95
B) 1.75
C) 1.86
D) 2

Solutions: