PRMIA 8002 - PRM Certification - Exam II: Mathematical Foundations of Risk Measurement Exam

Question #1 (Topic: )

Maximum likelihood estimation is a method for:

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

Answer: A

Question #2 (Topic: )

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. 10 B. 100 C. 25 D. 5

Answer: A

Question #3 (Topic: )

Let a, b and c be real numbers. Which of the following statements is true?

A. The commutativity of multiplication is defined by B. The existence of negatives is defined by C. The distributivity of multiplication is defined by D. The associativity of multiplication is defined by

Answer: C

Question #4 (Topic: )

I have $5m to invest in two stocks: 75% of my capital is invested in stock 1 which has price
100 and the rest is invested in stock 2, which has price 125. If the price of stock 1 falls to
90 and the price of stock 2 rises to 150, what is the return on my portfolio?

A. -2.50% B. -5% C. 2.50% D. 5%

Answer: A

Question #5 (Topic: )

The first derivative of a function f(x) is zero at some point, the second derivative is also
zero at this point. This means that:

A. f has necessarily a minimum at this point B. f has necessarily a maximum at this point C. f has necessarily neither a minimum nor a maximum at this point D. f might have either a minimum or a maximum or neither of them at this point

Answer: D

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