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PRMIA 8007 Exam Syllabus Topics:
| Section | Objectives |
|---|---|
| Linear Algebra | - Matrix Methods
|
| Statistical Analysis | - Descriptive and Inferential Statistics
|
| Risk Measurement Applications | - Quantitative Risk Analysis
|
| Numerical Methods | - Quantitative Techniques
|
| Regression and Time Series Analysis | - Modeling Techniques
|
| Probability Theory | - Fundamental Probability Concepts
|
| Calculus | - Differential and Integral Calculus
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Question 1
A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?
A. 7.12
B. 7.29
C. 6.59
D. 7.44
Question 2
Which of the following can be used to evaluate a regression model?
(i) Magnitude of R2
(ii) Magnitude of TSS (total sum of squares)
(iii) Tests for statistical significance
(iv) Sign and magnitude of each regression parameter
A. (i), (ii), and (iii)
B. (i), (ii), (iii), and (iv)
C. (i), (iii), and (iv)
D. (i) and (iv)
Question 3
Every covariance matrix must be positive semi-definite. If it were not then:
A. Some portfolios could have a negative variance
B. The associated correlation matrix would not be positive semi-definite
C. It could not be used to simulate correlated asset paths
D. All the above statements are true
Question 4
Suppose I trade an option and I wish to hedge that option for delta and vega. Another option is available to trade. To complete the hedge I would
A. trade the underlying in such a way as to make the portfolio delta neutral, and then trade the other option in such a way as to make the portfolio vega neutral.
B. trade the underlying in such a way as to make the portfolio delta and vega neutral.
C. trade the other option in such a way as to make the portfolio delta and vega neutral.
D. trade the other option in such a way as to make the portfolio vega neutral, and then trade the underlying in such a way as to make the portfolio delta neutral.
Question 5
Which statement regarding the matrix below is true?
A. It is positive definite
B. It is positive semi-definite
C. It is negative definite
D. It is not positive definite
Solutions:
| Question 1 Answer: A | Question 2 Answer: C | Question 3 Answer: D | Question 4 Answer: D | Question 5 Answer: D |
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