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PRMIA 8007 Exam Syllabus Topics:

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

Question 1

A quadratic form is

A. an algebraic expression in two variables, x and y, involving , , and terms.
B. a specific solution of the Black-Scholes pricing formula
C. an algebraic expression in two variables, x and y, involving , and terms.
D. defined as a positive definite Hessian matrix.

Question 2

You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

A. a continuously-compounded rate of 4%
B. a lump-sum payment of $22 500 on maturity (in five years)
C. a quarterly-compounded rate of 4.1%
D. an annually compounded rate of 4.15%

Question 3

In a 2-step binomial tree, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of d = 1/u. The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. Use the Cox, Ross, Rubinstein parameterization to find the risk neutral probability and hence find the value of a European put option with strike 102, given that the underlying price is currently 100.

A. 5.19
B. 4.18
C. 5.66
D. 6.31

Question 4

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 2 are correct
B. Statements 1 and 3 are correct
C. Statements 2 and 3 are correct
D. All three statements are correct

Question 5

The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A. None of the above
B. x = -1, y = 0
C. x = 5, y = 0
D. x = 0, y = 20

Solutions: