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

1. Which of the provided answers solves this system of equations?
2y - 3x = 3y +x
y2 + x2 = 68

A) x = -2; y = -8
B) x = 1; y = square root of 67
C) x = 2; y = 8
D) x = 2; y = -8

2. Find the roots, if they exist in the real numbers, of the quadratic equation

A) -4 and 2
B) 1 and 0
C) No real roots
D) 4 and -2

3. What is the sum of the first 20 terms of this sequence: 3, 5, 9, 17, 33, 65,...?

A) 1 048 574
B) 2 097 172
C) 2 097 170
D) 1 048 595

4. 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) 6.31
C) 5.19
D) 5.66

5. 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) 19.23
B) 17.33
C) 20.54
D) 18.75

Solutions: