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

1. A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A) 0.3483
B) None of these
C) 0.7367
D) 0.2646

2. What is a Hessian?

A) The vector of partial derivatives of a contingent claim
B) The point at which a minimum of a multidimensional function is achieved
C) A matrix of second derivatives of a function
D) Correlation matrix of market indices

3. Two vectors are orthogonal when:

A) their scalar product (sum product) is zero
B) one is a scalar multiple of the other
C) their determinant is zero
D) their components are linearly dependent

4. You invest $100 000 for 3 years at a continuously compounded rate of 3%. At the end of 3 years, you redeem the investment. Taxes of 22% are applied at the time of redemption. What is your approximate after-tax profit from the investment, rounded to $10?

A) $9420
B) $7350
C) $7230
D) $7100

5. 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) 0.5292
B) 0.5288
C) 0.5290
D) 0.5286

Solutions: