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PRMIA 8007 Exam Syllabus Topics:

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

1. 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) 4.18
B) 5.19
C) 6.31
D) 5.66

2. If the annual volatility of returns is 25% what is the variance of the quarterly returns?

A) None of the above
B) 0.0156
C) 0.0625
D) 0.1250

3. Kurtosis(X) is defined as the fourth centred moment of X, divided by the square of the variance of X.
Assuming X is a normally distributed variable, what is Kurtosis(X)?

A) 3
B) 1
C) 0
D) 2

4. Suppose a discrete random variable can take on the values -1, 0 and 1 each with a probability of 1/3. Then the mean and variance of the variable is

A) mean is 0, variance is 1/2
B) mean is 1/3, variance is 1/3
C) mean is 0, variance is 1/3
D) mean is 0, variance is 2/3

5. When calculating the implied volatility from an option price we use the bisection method and know initially that the volatility is somewhere between 1% and 100%. How many iterations do we need in order to determine the implied volatility with accuracy of 0.1%?

A) 10
B) 25
C) 5
D) 100

Solutions: