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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Calculus and Functions | 20% | - Multivariable calculus
|
| Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
| Probability Theory | 25% | - Random variables and distributions
|
| Statistics and Regression Analysis | 20% | - Linear regression
|
| Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Basics of risk modeling - Time value of money |
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
The determinant of a matrix X is equal 2. Which of the following statements is true?
- A. det(2X) = 2 det(X)
- B. det(2X) = det(X)2
- C. det(2X) = 4 det(X)
- D. det(2X) =
Correct Answer: C 🗳️
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. 19.23
- C. 18.75
- D. 17.33
Correct Answer: A 🗳️
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
Correct Answer: C 🗳️
Bond convexity is closely related to ...
- A. The sensitivity of the bond's present value with respect to yield
- B. The second derivative of the bond's present value with respect to yield
- C. The integral of the bond's present value with respect to yield
- D. The derivative of the bond's present value with respect to yield
Correct Answer: B 🗳️
At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?
- A. -0.666666667
- B. 2
- C. 2.66667
- D. 0
Correct Answer: C 🗳️
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