PRMIA 8007 - Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition

In a binomial tree lattice, at each step the underlying price can move up by a factor of u = 1.1 or down by a factor of . The continuously compounded risk free interest rate over each time step is 1% and there are no dividends paid on the underlying. The risk neutral probability for an up move is:

Which of the following statements concerning class intervals used for grouping of data is correct?

When grouping data, attention must be paid to the following with regards to class intervals:

1. Class intervals should not overlap

2. Class intervals should be of equal size unless there is a specific need to highlight data within a specific subgroup

3. The class intervals should be large enough so that they not obscure interesting variation within the group

A linear regression gives the following output:

Figures in square brackets are estimated standard errors of the coefficient estimates.

Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

Which of the following statements is true?

There are two portfolios with no overlapping of stocks or bonds. Portfolio 1 has 6 stocks and 6 bonds. Portfolio 2 has 4 stocks and 8 bonds. If we randomly select one stock, what is the probability that it came from Portfolio1?

Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:

You are to perform a simple linear regression using the dependent variable Y and the independent variable X (Y = a + bX). Suppose that cov(X,Y)=10, var(X)= 5, and that the mean of X is 1 and the mean of Y is 2. What are the values for the regression parameters a and b?

Exploring a regression model for values of the independent variable that have not been observed is most accurately described as…

What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?