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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 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) 20.54
C) 18.75
D) 19.23

2. Newton-Raphson iteration is used to find a solution of x5 - x3 + x = 1. If xn = 2, what is xn+1?

A) 1.638
B) 2.362
C) 0.377
D) 1.623

3. What is the probability of tossing a coin and getting exactly 2 heads out of 5 throws?

A) 10/32
B) 9/23
C) None of these
D) 8/15

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

A) Some portfolios could have a negative variance
B) It could not be used to simulate correlated asset paths
C) All the above statements are true
D) The associated correlation matrix would not be positive semi-definite

5. The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?

A) 1
B) None of the above
C) 0.5
D) 0

Solutions: