PRMIA 8007 - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?
Over four consecutive years fund X returns 1%, 5%, -3%, 8%. What is the average growth rate of fund X over this period?
An option has value 10 when the underlying price is 99 and value 9.5 when the underlying price is 101. Approximate the value of the option delta using a first order central finite difference.
For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)
Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24
Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.
The determinant of a matrix X is equal 2. Which of the following statements is true?
A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points
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?
Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?
