Deck 15: No Arbitrage and the Pricing of Interest Rate Securities

Question 1

How strong is the correlation among rates with different maturities in the term structure obtained from the CIR model?

Answer 1

As with the Vasicek model, the interest rates on the term structure are perfectly correlated.

Question 2

How can we obtain ? in order to calibrate the Vasicek model?

Answer 2

? can be estimated directly from the time series of interest rates rt.

Question 3

For a deterministic interest rate model, what would be the rate of return on securities? Explain.

Answer 3

Given no arbitrage:

Question 4

What are the three steps for derivative pricing and hedging?

Question 5

What is a Partial Differential Equation (PDE)?

Question 6

For the Vasicek model can we say that always m∗(r, t)=m(r, t)? Explain.

Question 7

What is a solution to a PDE?

Question 8

What's the intuition behind the following relationship:

Question 9

Why is it that in a deterministic interest rate world we have that:

Question 10

How can we obtain ¯r and ? in order to calibrate the Vasicek model?

Question 11

Does the following equality hold in the real world? Why or why not?

Question 12

How strong is the correlation among rates in the term structure obtained from the Vasicek model? Is this realistic?

Question 13

What relation should hold across all securities, given the no arbitrage condition?

Question 14

What do we need to build in order to be able to price any security through no arbitrage?

Question 15

IntheVasicekmodeldewehavelevel,slopeandcurvatureintheterm structure?

Question 16

Does the Vasicek model match the term structure?

Question 17

What problem does the Cox-Ingersol-Ross (CIR) model solve when com- pared to the Vasicek and Ho-Lee models?