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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Topic 2: Numerical Methods & Financial Mathematics | 15% | - Basics of risk modeling - Root finding and approximation - Time value of money |
| Topic 3: Probability Theory | 25% | - Random variables and distributions
|
| Topic 4: Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Topic 5: Calculus and Functions | 20% | - Multivariable calculus
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Variance reduction is:
- A. A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
- B. A method for reducing the number of simulations required in a Monte Carlo simulation
- C. A technique that is applied in regression models to improve the accuracy of the coefficient estimates
- D. A numerical method for finding the variance of the underlying that is implicit in a market price of an option
The bisection method can be used for solving f(x)=0 for a unique solution of x, when
- A. The function f(x) is continuous and monotonic
- B. The function f(x) is differentiable
- C. The function f(x) is differentiable and we have an explicit expression for the derivative
- D. The function f(x) is continuous
A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?
- A. 11.82
- B. 12.49
- C. 12.78
- D. 12.33
Simple linear regression involves one dependent variable, one independent variable and one error variable. In contrast, multiple linear regression uses...
- A. One dependent variable, many independent variables, one error variable
- B. Many dependent variables, one independent variable, one error variable
- C. Many dependent variables, many independent variables, many error variables
- D. One dependent variable, one independent variable, many error variables
A quadratic form is
- A. an algebraic expression in two variables, x and y, involving , , and terms.
- B. defined as a positive definite Hessian matrix.
- C. an algebraic expression in two variables, x and y, involving , and terms.
- D. a specific solution of the Black-Scholes pricing formula
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