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PRMIA 8007 Exam Syllabus Topics:

PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European put option has a strike of 105 and a maturity of 90 days. Its Black-Scholes price is 7.11. The options sensitivities are: delta = -0.59; gamma = 0.03; vega = 19.29. Find the delta-gamma approximation to the new option price when the underlying asset price changes to 105

A) 6.49
B) 4.59
C) 4.54
D) 5.03

2. Maximum likelihood estimation is a method for:

A) Estimating the implied volatility of a simple European option
B) Finding parameter estimates of a given density function
C) Estimating the solution of a partial differential equation
D) Solving a portfolio optimization problem

3. 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) in the interval ]-2,+[
B) in the interval ]-2.5,-2[
C) in the interval ]-,-2.5]
D) equal to -2

4. Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?

A) N(x) 0 as x
B) N'(0) 0
C) N'(x) 0 as x
D) N(0) = 0.5

5. Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8

A) x = -2, y = 2
B) x = 2, y = 0
C) x = 1, y = 0.5
D) None of the above

Solutions: