Problem 6.

This problem will ask you to calculate effective duration and convexity using a bino-

mial tree model.

Suppose we have the following interest rate tree:

1-year spot rate at time 0 is 6%

In each 1-year period, the 1-year spot rate can either go up by 10%, or down by 10%

The risk-neutral probabilities of the spot rate going up or down are both 50%

Assume annual compounding and annual coupon payments

(a) What is the price of a $100 par 5% coupon bond maturing in 2 years?

(b) What is the value of the bond in part (a) if it had a call option at Year 1 at a call price of $99?

(c) Recalculate the prices for the bonds in parts (a) and (b) if the initial spot rate,S0 was 5%.

(d) Recalculate the prices for the bonds in parts (a) and (b) if the initial spot rate,S0 was 7%.

(e) You have now calculated a total of 6 prices. These are the prices of the plain-vanilla bond and the callable bond for initial 1-year spot rates of 5%, 6%, and 7%. On the same graph, plot the prices of the two bonds against these initial spot rates.