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

1. Every covariance matrix must be positive semi-definite. If it were not then:

A) One or more of its eigenvalues would be negative
B) There would be no Cholesky decomposition matrix
C) Some portfolios could have a negative variance
D) All the above statements are true

2. A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2%. What is the value of the option in this model?

A) 12.78
B) 11.82
C) 12.49
D) 12.33

3. Let a, b and c be real numbers. Which of the following statements is true?

A) The commutativity of multiplication is defined by
B) The distributivity of multiplication is defined by
C) The associativity of multiplication is defined by
D) The existence of negatives is defined by

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) 18.75
D) 20.54

5. Consider two securities X and Y with the following 5 annual returns:
X: +10%, +3%, -2%, +3%, +5%
Y: +7%, -2%, +3%, -5%, +10%
In this case the sample covariance between the two time series can be calculated as:

A) 0.00087
B) 0.00109
C) 0.40729
D) 0.32583

Solutions: