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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) Estimating the implied volatility of a simple European option
C) Estimating the solution of a partial differential equation
D) Solving a portfolio optimization problem

2. Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter

A) (i), (ii), and (iii)
B) (i), (iii), and (iv)
C) (i), (ii), (iii), and (iv)
D) (i) and (iv)

3. If a time series has to be differenced twice in order to be transformed into a stationary series, the original series is said to be:

A) integrated of order 2
B) non-functional
C) non-linear
D) differential

4. When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

A) 25
B) 5
C) 10
D) 100

5. Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade. To complete the hedge I would

A) trade the underlying in such a way as to make the portfolio delta neutral, and then trade the other option in such a way as to make the portfolio vega neutral.
B) trade the underlying in such a way as to make the portfolio delta and vega neutral.
C) trade the other option in such a way as to make the portfolio delta and vega neutral.
D) trade the other option in such a way as to make the portfolio vega neutral, and then trade the underlying in such a way as to make the portfolio delta neutral.

Solutions: