The one-year LIBOR rate is 3% and the forward rate for the one- to two-year period is 3.2%. The three-year swap rate for a swap with annual payments is 3.2%. What is the LIBOR forward rate for the 2 to 3 year period if OIS zero rates for one, two, and three year maturities are 2.5%, 2.7%, and 2.9%, respectively

$2.27 million

Explanation:

Calculation for What is the value of a three-year swap where 4% is received and LIBOR is paid on a principal of $100 million

First step is to calculate the value of the first

exchange

Value of the first exchange=0.032-0.030/1.025

Value of the first exchange=0.002/1.025

Value of the first exchange=0.001951

Second step is to calculate the value of the second exchange

Value of the second exchange=0.032-0.032/1.027^2

Value of the Second exchange=0.00

Third step is to calculate the value of the third exchange

Value of the third exchange=0.032-R/1.029^3

0.032-R/1.029^3=-0.001951

Hence R=0.0034126

In a situation where a swap of 4% is been received on a principal amount of $100 million

it will either provides 0.8% of $100 million or

the amount of $800,000 per year more than a swap that is worth zero which means that Its value be calculated as :

Value of the swap =800,000/1.025+800,000/1.027^2+800,000/1.029^3

Value of the swap =780,487.80+758,488.67+734,249.84

Value of the swap =$2,273,226.32

Value of the swap=$2.27 million

Therefore the valueof a three-year swap where 4% is received and LIBOR is paid on a principal of $100 million will be $2.27 million