• Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Certification Provider: PRMIA
  • Corresponding Certification:PRM
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PRMIA 8007 Exam Syllabus Topics:

SectionWeightObjectives
Linear Algebra and Matrix Theory20%- Vectors and eigenvalues
  • 1. Diagonalization
    • 2. Eigenvalues and eigenvectors
      - Matrix operations
      • 1. Determinants and trace
        • 2. Addition, multiplication, inversion
          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
                  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
                          Calculus and Functions20%- Single-variable calculus
                          • 1. Integrals and applications
                            • 2. Derivatives and applications
                              • 3. Limits and continuity
                                - Multivariable calculus
                                • 1. Partial derivatives
                                  • 2. Optimization
                                    Numerical Methods & Financial Mathematics15%- Time value of money
                                    - Root finding and approximation
                                    - Basics of risk modeling

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

                                    Question 1

                                    The fundamental theorem of analysis establishes a relation between

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


                                    Question 2

                                    Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

                                    A. negative
                                    B. not defined
                                    C. positive
                                    D. zero


                                    Question 3

                                    What is the simplest form of this expression: log2(165/2)

                                    A. log2 (5/2) + log2(16)
                                    B. 10
                                    C. 5/2 + log2(16)
                                    D. 32


                                    Question 4

                                    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. -0.5
                                    B. -4
                                    C. -0.25
                                    D. 0.25


                                    Question 5

                                    The sum of the infinite series 1+1/2+1/3+1/4+1/5+.... equals:

                                    A. 20
                                    B. 128
                                    C. Infinity
                                    D. 12


                                    Solutions:

                                    Question 1
                                    Answer: D
                                    Question 2
                                    Answer: D
                                    Question 3
                                    Answer: B
                                    Question 4
                                    Answer: C
                                    Question 5
                                    Answer: C

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