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PRMIA 8007 Exam Syllabus Topics:

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

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

                                    1. Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

                                    A) -1.2
                                    B) None of the above
                                    C) -2.8
                                    D) 1.3


                                    2. Consider an investment fund with the following annual return rates over 8 years: +6%, -6%, +12%, -12%,
                                    +3%, -3%, +9%, -9% .
                                    What can you say about the annual geometric and arithmetic mean returns of this investment fund?

                                    A) The arithmetic mean return is zero and the geometric mean return is negative
                                    B) The arithmetic mean return is equal to the geometric mean return
                                    C) None of the above
                                    D) The arithmetic mean return is negative and the geometric mean return is zero


                                    3. An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101.
                                    Approximate the value of the option delta using a first order central finite difference.

                                    A) -0.25
                                    B) -4
                                    C) 0.25
                                    D) -0.5


                                    4. Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by

                                    A) f(x)G(x) - F(x)g'(x)dx
                                    B) F(x)g(x) - F(x)g'(x)dx
                                    C) F(x)g(x) + f(x)G(x)
                                    D) F(x)G(x)


                                    5. A linear regression gives the following output:
                                    Figures in square brackets are estimated standard errors of the coefficient estimates. What is the value of the test statistic for the hypothesis that the coefficient of is zero against the alternative that is less than zero?

                                    A) -1.25
                                    B) 2.5
                                    C) -2.5
                                    D) 0.125


                                    Solutions:

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

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