The current oneyear and twoyear libor rates are 11 and 12 re

The current one-year and two-year libor rates are 1.1% and 1.2%, respectively. (a) What is the price of a ZCB maturing in 2 years? (b) What is the quarterly compounded one-year forward one-year rate?

Solution

a) A ZCB after 2 years will be say 100 rs. We have to consider annual compounding at a rate of 1.2% annually for 2 years;

Thus: x* (1.012)^2= 100; Thus x= 100/ (1.012)^2= 97.64252

Thus the price of a ZCB of face value 100 would be 97.64252

b) If it is compunded quarterly then the 1.1% annual libor rate would effectively be 1.1/4= 0.275% quarterly libor rate; So the yearly libor rate would be (1+0.00275)⁴=1.01104545 which means 1.104545 % one year forward one year rate;

Thus quarterly compounded one year forward one year rate = 1.104545%