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PRMIA 8007 Exam Syllabus Topics:

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 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) 4.54
B) 4.59
C) 6.49
D) 5.03

2. The fundamental theorem of analysis establishes a relation between

A) The derivative of a function and the slope of its graph
B) The derivative of a function and the derivative of its inverse function
C) Integration and differentiation of functions
D) First and second derivative of a function

3. Suppose we perform a principle component analysis of the correlation matrix of the returns of 13 yields along the yield curve. The largest eigenvalue of the correlation matrix is 9.8. What percentage of return volatility is explained by the first component? (You may use the fact that the sum of the diagonal elements of a square matrix is always equal to the sum of its eigenvalues.)

A) 64%
B) Cannot be determined without estimates of the volatilities of the individual returns
C) 98%
D) 75%

4. Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?

A) The lattice will not recombine
B) There will always be a downward drift in the lattice
C) The probability of an up move will not be constant
D) None of the above

5. An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?

A) 0.02
B) 0.50
C) 0.14
D) 0.25

Solutions: