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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Calculus and Functions | 20% | - Single-variable calculus
|
| Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
| Numerical Methods & Financial Mathematics | 15% | - Basics of risk modeling - Time value of money - Root finding and approximation |
| Probability Theory | 25% | - Basic probability concepts
|
| Statistics and Regression Analysis | 20% | - Descriptive statistics
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Question 1
The determinant of a matrix X is equal 2. Which of the following statements is true?
A. det(2X) = 4 det(X)
B. det(2X) = 2 det(X)
C. det(2X) =
D. det(2X) = det(X)2
Question 2
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. 20.54
B. 18.75
C. 17.33
D. 19.23
Question 3
What is the maximum value for f(x)= 8-(x+3)(x-3)?
A. 8
B. None of these
C. -1
D. 17
Question 4
What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?
A. 2 097 170
B. 1 048 574
C. 2 097 172
D. 1 048 595
Question 5
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 = SD()/MEAN(), t distribution
D. test statistic = MEAN()/SD(), t distribution
Solutions:
| Question 1 Answer: A | Question 2 Answer: A | Question 3 Answer: D | Question 4 Answer: A | Question 5 Answer: D |
