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

8007
  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Sep 16, 2026
  • Q & A: 133 Questions and Answers

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PRMIA 8007 Exam Syllabus Topics:

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

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

                              Question #1

                              Every covariance matrix must be positive semi-definite. If it were not then:

                              • A. Some portfolios could have a negative variance
                              • B. It could not be used to simulate correlated asset paths
                              • C. All the above statements are true
                              • D. The associated correlation matrix would not be positive semi-definite
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              Question #2

                              An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European call option has a strike of 85 and a maturity of 40 days. Its Black-Scholes price is 15.52. The options sensitivities are: delta = 0.98; gamma = 0.006 and vega = 1.55. What is the delta-gamma-vega approximation to the new option price when the underlying asset price changes to 105 and the volatility changes to 28%?

                              • A. 20.54
                              • B. 19.23
                              • C. 17.33
                              • D. 18.75
                              Reveal Solution  Discussion  0

                              Correct Answer: A  🗳️

                              Question #3

                              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. None of these
                              • B. 0.7367
                              • C. 0.2646
                              • D. 0.3483
                              Reveal Solution  Discussion  0

                              Correct Answer: D  🗳️

                              Question #4

                              On average, one trade fails every 10 days. What is the probability that no trade will fail tomorrow?

                              • A. 0.100
                              • B. 0.095
                              • C. 0.905
                              • D. 0.95
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

                              Question #5

                              An indefinite integral of a polynomial function is

                              • A. none of the above
                              • B. always positive
                              • C. always less than the function itself
                              • D. always increasing
                              Reveal Solution  Discussion  0

                              Correct Answer: A  🗳️

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