PRMIA 8007 Valid Q&A - in .pdf

  • 8007 pdf
  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Jul 26, 2026
  • Q & A: 133 Questions and Answers
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  • Updated: Jul 26, 2026
  • Q & A: 133 Questions and Answers
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  • 8007 Testing Engine
  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
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PRMIA 8007 Exam Syllabus Topics:

SectionWeightObjectives
Topic 1: Numerical Methods & Financial Mathematics15%- Root finding and approximation
- Basics of risk modeling
- Time value of money
Topic 2: Probability Theory25%- Random variables and distributions
  • 1. Expected value, variance, covariance
    • 2. Discrete and continuous distributions
      - Basic probability concepts
      • 1. Conditional probability and independence
        • 2. Axioms and rules
          Topic 3: Statistics and Regression Analysis20%- Descriptive statistics
          • 1. Measures of location and dispersion
            • 2. Correlation and covariance
              - Linear regression
              • 1. Hypothesis testing and confidence intervals
                • 2. Simple and multiple regression
                  Topic 4: Calculus and Functions20%- Multivariable calculus
                  • 1. Optimization
                    • 2. Partial derivatives
                      - Single-variable calculus
                      • 1. Integrals and applications
                        • 2. Limits and continuity
                          • 3. Derivatives and applications
                            Topic 5: Linear Algebra and Matrix Theory20%- Matrix operations
                            • 1. Addition, multiplication, inversion
                              • 2. Determinants and trace
                                - Vectors and eigenvalues
                                • 1. Diagonalization
                                  • 2. Eigenvalues and eigenvectors

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

                                    1. In a quadratic Taylor approximation, a function is approximated by:

                                    A) a parabola
                                    B) a cubic polynomial
                                    C) a constant
                                    D) a straight line


                                    2. Find the roots, if they exist in the real numbers, of the quadratic equation

                                    A) -4 and 2
                                    B) No real roots
                                    C) 4 and -2
                                    D) 1 and 0


                                    3. You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?

                                    A) test statistic = MEAN()/SD(), normal distribution
                                    B) test statistic = SD()/MEAN(), normal distribution
                                    C) test statistic = MEAN()/SD(), t distribution
                                    D) test statistic = SD()/MEAN(), t distribution


                                    4. 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) 17.33
                                    B) 19.23
                                    C) 20.54
                                    D) 18.75


                                    5. What is the maximum value for f(x)= 8-(x+3)(x-3)?

                                    A) 17
                                    B) None of these
                                    C) -1
                                    D) 8


                                    Solutions:

                                    Question # 1
                                    Answer: A
                                    Question # 2
                                    Answer: B
                                    Question # 3
                                    Answer: C
                                    Question # 4
                                    Answer: C
                                    Question # 5
                                    Answer: A

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