PRMIA 8007 Exam Questions : Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Nov 04, 2026
  • Q&As: 133 Questions and Answers

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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Probability and Statistics Foundations- Random variables and probability distributions
  • 1. Expectation, variance, and moments
    • 2. Discrete and continuous distributions
      - Statistical inference
      • 1. Estimation theory
        • 2. Confidence intervals and hypothesis testing
          Stochastic Processes and Time Series- Stochastic processes basics
          • 1. Markov processes
            • 2. Brownian motion (introductory level)
              - Time series analysis
              • 1. Autocorrelation and stationarity
                • 2. AR, MA, and ARMA models
                  Simulation and Numerical Methods- Monte Carlo simulation
                  • 1. Risk distribution simulation
                    • 2. Random number generation
                      Risk Measurement Techniques- Value at Risk (VaR)
                      • 1. Historical simulation approach
                        • 2. Parametric and non-parametric VaR
                          - Volatility and correlation
                          • 1. Correlation estimation techniques
                            • 2. Variance-covariance methods

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

                              Question #1

                              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. 0.5288
                              • B. 0.5290
                              • C. 0.5286
                              • D. 0.5292
                              Reveal Solution  Discussion  0

                              Correct Answer: A  🗳️

                              Question #2

                              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. 5%
                              • B. 2.50%
                              • C. -5%
                              • D. -2.50%
                              Reveal Solution  Discussion  0

                              Correct Answer: D  🗳️

                              Question #3

                              The correlation between two asset returns is 0.5. What is the largest eigenvalue of their correlation matrix?

                              • A. 0.5
                              • B. 1.5
                              • C. 1
                              • D. None of the above
                              Reveal Solution  Discussion  0

                              Correct Answer: B  🗳️

                              Question #4

                              What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

                              • A. 1 / (x+y)
                              • B. ln(x+y) x + ln(x+y) y
                              • C. -x/(x+y) - y/(x+y)
                              • D. (x + y) / (x+y)
                              Reveal Solution  Discussion  0

                              Correct Answer: D  🗳️

                              Question #5

                              The fundamental theorem of analysis establishes a relation between

                              • A. First and second derivative of a function
                              • B. Integration and differentiation of functions
                              • C. The derivative of a function and the derivative of its inverse function
                              • D. The derivative of a function and the slope of its graph
                              Reveal Solution  Discussion  0

                              Correct Answer: B  🗳️

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