The on-the-run issue for ABC Company is shown below:
Maturity Yield to maturity Market price
1 7.50% 100
2 7.60% 100
3 7.70% 100
Using the bootstrapping methodology, the spot rates are:
Maturity Spot rate
1 7.50%
2 7.604%
3 7.71%
Assuming an interest rate volatility of 10% for the 1-year rate, the binomial interest rate tree for valuing a bond with maturity of up to three years is shown below:
7.50%
8.481%
6.944%
9.603%
7.862%
6.437%
a) Demonstrate using the 3-year on-the-run issue that the binomial interest rate tree above is in fact an arbitrage free tree.
b) Consider a 2-year on-the-run issue, demonstrate that the binomial interest rate tree above is also an arbitrage free tree
c) Using the spot rate given above, what is the arbitrage-free value of a 3-year 8.5% coupon issue of ABC Company
d) Using the binomial tree, determine the value of an 8.5% 3-year option free- bond
e) Suppose that the 3-year 8.5% is callable starting in year 1 at par (100). What is the value of this 3-year 8.5% coupon callable bond?
f) What is the value of embedded call option for the 3-year 8.5% callable issue?