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

1. Stress testing portfolios requires changing the asset volatilities and correlations to extreme values. Which of the following would lead to a non positive definite covariance matrix?

A) Changing all the correlations to be zero
B) All of the above
C) Changing the volatilities to be greater than 100%
D) Changing all the correlations to be unity

2. 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) 20.54
B) 19.23
C) 18.75
D) 17.33

3. Variance reduction is:

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

4. Which of the following statements is not correct?

A) A function is defined by its domain together with its action.
B) A function is a rule that assigns to every value x at least one value of y.
C) For finite and small domains, the action of a function may be specified by a list.
D) Every linear function is also a quadratic function.

5. A 2-step binomial tree is used to value an American put option with strike 105, given that the underlying price is currently 100. At each step the underlying price can move up by 10 or down by 10 and the risk-neutral probability of an up move is 0.6. There are no dividends paid on the underlying and the continuously compounded risk free interest rate over each time step is 1%. What is the value of the option in this model?

A) 7.44
B) 7.12
C) 6.59
D) 7.29

Solutions: