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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Probability Theory | 25% | - Basic probability concepts
|
| Topic 2: Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
| Topic 3: Numerical Methods & Financial Mathematics | 15% | - Basics of risk modeling - Time value of money - Root finding and approximation |
| 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:
1. On average, one trade fails every 10 days. What is the probability that no trade will fail tomorrow?
A) 0.095
B) 0.100
C) 0.905
D) 0.95
2. In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.
A) 4.18
B) 5.19
C) 6.31
D) 5.66
3. When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?
A) 5
B) 10
C) 25
D) 100
4. Which of the following is consistent with the definition of a Type I error?
A) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of no correlation was rejected
B) A Type I occurs whenever data series are serially correlated
C) The probability of a Type I error is 100% minus the significance level
D) A Type I error would have occurred if the performance of a stock was positively correlated with the performance of a hedge fund, but in a linear regression, the hypothesis of positive correlation was rejected
5. Which of the following is not a direct cause of autocorrelation or heteroskedasticity in the residuals of a regression model?
A) A high positive correlation between two explanatory variables
B) Using an inappropriate functional form in the model
C) A structural break in the dependent variable
D) The omission of a relevant explanatory variable
Solutions:
| Question # 1 Answer: C | Question # 2 Answer: C | Question # 3 Answer: B | Question # 4 Answer: D | Question # 5 Answer: A |
