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

1. A biased coin has a probability of getting heads equal to 0.3. If the coin is tossed 4 times, what is the probability of getting heads at least two times?

A) 0.2646
B) 0.7367
C) None of these
D) 0.3483


2. The bisection method can be used for solving f(x)=0 for a unique solution of x, when

A) The function f(x) is continuous
B) The function f(x) is continuous and monotonic
C) The function f(x) is differentiable and we have an explicit expression for the derivative
D) The function f(x) is differentiable


3. You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?

A) The commodity returns are integrated of order 1
B) The commodity returns are stationary
C) None of the above
D) The commodity prices are stationary


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) 18.75
C) 19.23
D) 20.54


5. A 95% confidence interval for a parameter estimate can be interpreted as follows:

A) The probability that the estimated value of the parameter is within this interval is 95%.
B) The probability that the estimated value of the parameter is outside this interval is 95%.
C) The probability that the real value of the parameter is outside this interval is 95%.
D) The probability that the real value of the parameter is within this interval is 95%.


Solutions:

Question # 1
Answer: D
Question # 2
Answer: B
Question # 3
Answer: C
Question # 4
Answer: D
Question # 5
Answer: D

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