Deck 22: Multifactor Models

Question 1

Is the 2-factor Vasicek model an afine model?

Answer 1

Yes, it is an afine model. It allows a closed form solution.

Question 2

What are multifactor models?

Answer 2

Multifactor models are models that allow for more than one factor (that is in addition to the interest rate) to be defined by a stochastic process.

Question 3

Show that, given:

Answer 3

Question 4

In the Vasicek one factor model, the short rate determines the model. In the Vasicek two factor model, what rates drive the model?

Question 5

Does the 2-factor Vasicek model fit the yield curve?

Question 6

Given that we now have two stochastic factors, when writing Ito's lemma as the following what are we implicitly assuming about them?

Question 7

Why is it considered that implied volatility of interest rate options has a "hump" shape?

Question 8

What peculiarity of a yield curve steepner makes the use of 2-factor models attractive?

Question 9

When are multifactor models used?

Question 10

What modi?cations should be included to Ito's lemma when we allow correlation between the two factors?

Question 11

How is the multivariate Ito's lemma defined?

Question 12

Can a solution always be found in order to price a security as proposed by the Feynman-Kac formula?

Question 13

In the 2-factor Hull-White model, what is the benefit of introducing θt (time dependent central tendency)?

Question 14

Under the Vasicek model, what degree of correlation do different interest rates have?

Question 15

What advantages does the 2-factor Vasicek have when fitting volatility?

Question 16

What is the difference between using a model for finding arbitrage oppor- tunities and using a model for pricing derivatives and other securities?