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

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Total 132 questions

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

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

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

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

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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Total 132 questions