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

1. Maximum likelihood estimation is a method for:

A) Finding parameter estimates of a given density function
B) Solving a portfolio optimization problem
C) Estimating the implied volatility of a simple European option
D) Estimating the solution of a partial differential equation

2. A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

A) 12.33
B) 12.78
C) 11.82
D) 12.49

3. In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

A) 5/7
B) 6/11
C) 8/11
D) None of these

4. Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?

A) The lattice will not recombine
B) There will always be a downward drift in the lattice
C) None of the above
D) The probability of an up move will not be constant

5. If A and B are two events with P(A) = 1/4, P(B) = 1/3 and P(A intersection B) =1/5, what is P(Bc | Ac) i.e. the probability of the complement of B when the complement of A is given?

A) 12/29
B) 3/4
C) 37/45
D) None of these

Solutions: