Deck 9: One Step Binomial Trees

Question 1

What is the risk neutral probability p∗ ofthetreepresented?

Answer 1

We have that p∗ = 0.7038.

Question 2

Are forward interest rates equal to the market's expectation of future interest rates?

Answer 2

No. Current high forward rates might mean two things: either market participants expect higher interest rates; or they are strongly averse to risk, and thus the price of long term bonds is low today.

Question 3

Using risk neutral pricing obtain the value for a European option on inter- est rates with maturity at t =0.5, rK =1.5% and payo?: 100 × max(rt ? rK, 0).

Answer 3

The price is 1.7419.

Question 4

You are given the following interest rate tree. Use it when required in the
exercises.
What is a replicating portfolio?

Question 5

Given the tree at the begining of this chapter, what is the value of a zero coupon bond maturing in six months?

Question 6

Assuming that there is a risk premium in the market (people worry about risk and expect to be compensated for it), is risk neutral probability for an up state (high interest rates) higher, lower or the same as the risk natural probability?

Question 7

from a given risk neutral tree can you compute the mar- ket participants' expectation on the level of interest rates in the future? Explain.

Question 8

You are given the following interest rate tree. Use it when required in the
exercises.
What is the favored approach in the development of interest rate models? CAPM?

Question 9

For pricing purposes how important is it to know the true probabilities?

Question 10

Why are forward interst rates and the risk neutral expected future interest rates not the same?

Question 11

What is a risk neutral probability?

Question 12

What is the market price of risk?

Question 13

What is the market price of risk underlying the tree presented?

Question 14

What is risk neutral pricing?

Question 15

What values can a one year zero coupon bond take at t =0.5?