Deck 14: Interest Rate Models in Continuous Time

Question 1

What two components do we include in a Continous Time Stochastic Pro- cess?

Answer 1

We include a Brownian motion and a Differential Equation.

Question 2

What is the Martingale property?

Answer 2

Question 3

What is Ito's Lemma?

Answer 3

Ito's Lemma provides the "rules" of calculus to link the variation of an underlying stochastic variable, such as the interest rate rt, to the price of securities that depend on it.

Question 4

What is a solution to an Ordinary Differential Equation?

Question 5

When dealing with a stochastic process what do we mean by a 'drift'?

Question 6

Show that:

Question 7

What are the properties of a Brownian motion?

Question 8

What is a differential equation?

Question 9

Why do we need continous time models?

Question 10

What is a Brownian motion?

Question 11

What is the main difference between the Ho-Lee and the Vasicek model?

Question 12

What problem do both Vasicek and Ho-Lee models share?

Question 13

You put money into the stock market because you expect to make a profit (although you might loose money). Does your capital follow a Martingale?

Question 14

When dealing with a stochastic process what do we mean by a 'diffusion'?

Question 15

According to Ito's Lemma, what are the three components of the drift term in an asset?