Please see attachment for tables and pre-question information.
Suppose the following coupon info
Maturity (year) Coupon Rate price
1 0% 97
2 3.00% 99
2 0% 91
3 4.00% 98
3 0% 87
Please note there are arbitrage opportunities (shown below).
The 1-yr rate implied by the 1-yr zero coupon bound is
= 100/97 - 1 = 3.09%
The 2-yr rate implied by the 2-yr zero coupon bound is
91 = 100/ = - 1 = 4.828%
The 2-yr rate implied by the 2-yr coupon bound is
99 = = 3.5%
The 3-yr rate implied by the 3-yr zero coupon bound is
87 = 100/ = - 1 = 4.75%
The 3-yr rate implied by the 3-yr coupon bound is
98 = = 4.75%
The 2-year rates implied by coupon bond is different to those implied by zero coupon bonds. Hence there is arbitrage opportunity for this segment of term structure.
1. Is there any other arbitrage opportunity?
2. Given above bonds, what are the implied forward rates?
3. If one was to invest $1,000 two years from now for one year. Which would be the best strategy (what forward rate to use)? What is the return?
The solution identifies arbitrage opportunities and calculates the implied forward rates.