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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Topic 1: Probability Theory- Fundamental Probability Concepts
  • 1. Random Variables
  • 2. Bayes' Theorem
  • 3. Probability Rules
  • 4. Conditional Probability
Topic 2: Linear Algebra- Matrix Methods
  • 1. Positive Definiteness
  • 2. Covariance Matrices
  • 3. Matrix Operations
  • 4. Eigenvalues and Eigenvectors
Topic 3: Regression and Time Series Analysis- Modeling Techniques
  • 1. Multivariate Regression
  • 2. Time Series Forecasting
  • 3. Linear Regression
  • 4. Model Diagnostics
Topic 4: Risk Measurement Applications- Quantitative Risk Analysis
  • 1. Value at Risk Methodologies
  • 2. Volatility Modeling
  • 3. Portfolio Risk Measurement
  • 4. Sensitivity Analysis
Topic 5: Numerical Methods- Quantitative Techniques
  • 1. Optimization Methods
  • 2. Monte Carlo Methods
  • 3. Numerical Approximation
  • 4. Simulation Techniques
Topic 6: Calculus- Differential and Integral Calculus
  • 1. Differentiation
  • 2. Integration
  • 3. Functions and Limits
  • 4. Multivariable Calculus
Topic 7: Statistical Analysis- Descriptive and Inferential Statistics
  • 1. Maximum Likelihood Estimation
  • 2. Hypothesis Testing
  • 3. Confidence Intervals
  • 4. Moments and Distributions

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

Question #1

Which of the following statements about variance and standard deviation are correct?
1. When calculated based on a sample of the population data, one has to correct for any bias in the result by using the number of degrees of freedom in the calculation
2. Variance is in square root units of the underlying data, whereas standard deviation is in units of the underlying data
3. When considering independent variables, variance is additive, while standard deviation is not

  • A. Statements 1 and 3 are correct
  • B. All three statements are correct
  • C. Statements 1 and 2 are correct
  • D. Statements 2 and 3 are correct
Reveal Solution  Discussion  0

Correct Answer: A  🗳️

Question #2

In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others. What is the probability that an AA bond or a Corporate bond outperforms all of the others?

  • A. 5/7
  • B. None of these
  • C. 6/11
  • D. 8/11
Reveal Solution  Discussion  0

Correct Answer: B  🗳️

Question #3

Assume that 40% of all financial organizations investigated by authorities turn out to be fraudulent.
What is the probability of randomly investigating 2 different organizations and finding that neither is fraudulent; and what is the probability of finding exactly one being fraudulent?

  • A. 1/3 and 8/17
  • B. 2/5 and 3/5
  • C. 9/25 and 12/25
  • D. 2/5 and 1/2
Reveal Solution  Discussion  0

Correct Answer: C  🗳️

Question #4

Which of the following statements concerning class intervals used for grouping of data is correct?
When grouping data, attention must be paid to the following with regards to class intervals:
1. Class intervals should not overlap
2. Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup
3. The class intervals should be large enough so that they not obscure interesting variation within the group

  • A. Statements 1 and 3 are correct
  • B. All three statements are correct
  • C. Statements 1 and 2 are correct
  • D. Statements 2 and 3 are correct
Reveal Solution  Discussion  0

Correct Answer: C  🗳️

Question #5

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
Reveal Solution  Discussion  0

Correct Answer: D  🗳️

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