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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Basics of risk modeling - Time value of money |
| Topic 2: Probability Theory | 25% | - Random variables and distributions
|
| Topic 3: Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Topic 4: Calculus and Functions | 20% | - Multivariable calculus
|
| Topic 5: Linear Algebra and Matrix Theory | 20% | - Matrix operations
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
1. In a quadratic Taylor approximation, a function is approximated by:
A) a parabola
B) a cubic polynomial
C) a constant
D) a straight line
2. Find the roots, if they exist in the real numbers, of the quadratic equation
A) -4 and 2
B) No real roots
C) 4 and -2
D) 1 and 0
3. 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 = MEAN()/SD(), t distribution
D) test statistic = SD()/MEAN(), t distribution
4. 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) 17.33
B) 19.23
C) 20.54
D) 18.75
5. What is the maximum value for f(x)= 8-(x+3)(x-3)?
A) 17
B) None of these
C) -1
D) 8
Solutions:
| Question # 1 Answer: A | Question # 2 Answer: B | Question # 3 Answer: C | Question # 4 Answer: C | Question # 5 Answer: A |





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