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PRMIA 8007 Exam Syllabus Topics:
| Section | Objectives |
|---|---|
| Topic 1: Stochastic Processes and Time Series | - Stochastic processes basics
|
| Topic 2: Simulation and Numerical Methods | - Monte Carlo simulation
|
| Topic 3: Probability and Statistics Foundations | - Random variables and probability distributions
|
| Topic 4: Risk Measurement Techniques | - Value at Risk (VaR)
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
A 95% confidence interval for a parameter estimate can be interpreted as follows:
- A. The probability that the real value of the parameter is within this interval is 95%.
- B. The probability that the real value of the parameter is outside this interval is 95%.
- C. The probability that the estimated value of the parameter is within this interval is 95%.
- D. The probability that the estimated value of the parameter is outside this interval is 95%.
Correct Answer: A 🗳️
You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...
- A. equal to -2
- B. in the interval ]-,-2.5]
- C. in the interval ]-2.5,-2[
- D. in the interval ]-2,+[
Correct Answer: D 🗳️
Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?
- A. E(exp(X)) = 2.7183
- B. E(exp(X)) = 1
- C. E(exp(X)) = 0.6065
- D. E(exp(X)) = 1.6487
Correct Answer: D 🗳️
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. 6.31
- B. 4.18
- C. 5.66
- D. 5.19
Correct Answer: A 🗳️
Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?
- A. 2/5 and 3/5
- B. 9/25 and 12/25
- C. 2/5 and 1/2
- D. 1/3 and 8/17
Correct Answer: B 🗳️
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