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8007
  • Exam Code: 8007
  • Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
  • Updated: Jun 17, 2026
  • No. of Questions: 133 Questions and Answers
  • Download Limit: Unlimited
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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.

A) (i) only
B) (i) and (ii)
C) (i), (ii), and (iii)
D) (i) and (iii)


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

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


3. Variance reduction is:

A) A numerical method for finding portfolio weights to minimize the variance of a portfolio that has a given expected return
B) A numerical method for finding the variance of the underlying that is implicit in a market price of an option
C) A method for reducing the number of simulations required in a Monte Carlo simulation
D) A technique that is applied in regression models to improve the accuracy of the coefficient estimates


4. 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


5. What is a Hessian?

A) The vector of partial derivatives of a contingent claim
B) Correlation matrix of market indices
C) A matrix of second derivatives of a function
D) The point at which a minimum of a multidimensional function is achieved


Solutions:

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

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