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PRMIA 8007 Exam Syllabus Topics:

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

1. At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A) 0
B) 2.66667
C) 2
D) -0.666666667

2. A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?

A) 7.29
B) 7.44
C) 7.12
D) 6.59

3. 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) 4.59
B) 6.49
C) 4.54
D) 5.03

4. An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101.
Approximate the value of the option delta using a first order central finite difference.

A) 0.25
B) -0.5
C) -4
D) -0.25

5. I have a portfolio of two stocks. The weights are equal. The one volatility is 30% while the other is 40%. The minimum and maximum possible values of the volatility of my portfolio are:

A) 10% and 70%
B) 30% and 40%
C) 10% and 40%
D) 5% and 35%

Solutions: