Question

a) Find the price on an FRA(5x8) contract if the 5-month and 8-month spot LIBOR rates are 1.40% and 1.50% per year, respectively. Assume that the 5-month spot rate is for 152 days and the 8-month rate is for 243 days.

b) Briefly explain under what circumstances a buyer of an FRA contract profits from her position. Specifically, would a buyer make a profit from the position if LIBOR rates were to subsequently go up or down? No calculations are necessary, but using an FRA payoff equation would be useful here.

c) Now suppose that you buy the FRA contract at the rate you found in part (a) and exactly 60 days have passed. The current 3- and 6-month LIBOR rates are 1.55% and 1.65% per year, respectively. Determine the net present value of your contract if its notional principal was $100 million.

Answer 1

a) 5 month libor rate(152 days) = 1.4%

8 month libor rate(243 days) = 1.5%

Rate on a 5x8 FRA = [{1+ (8 month libor x 243/365)] / [1 +(5 month libor x 152/365)} -1} x 365/91

= [{1+(0.015 x 243/365)} / [1+(0.014 x 152/365)} - 1 ]x 365/91

=   [1.00413 -1] x 365/91

= 0.01657 = 1.66%

b) When the price of an FRA contract goes up, the buyer of the FRA profits as he would be getting a pay off equal to the new interest on the contract - the old interest on the contract multiplied by the notional value and the new interest rate is higher the buyer will have a cash inflow and the contract would be in profit.

Payoff on a FRA = (New FRA interest rate - Old FRA interest rate) x notional value.

c) If after 60 days

3 months libor (92 days) = 1.55%

6 month libor (183 days ) = 1.65%

The FRA has 3 months to maturity and the loan is of 3 months

So the new 3 x 3 FRA rate = [{1+ (6 month libor x 183/365)] / [1 +(3 month libor x 92/365)} -1} x 365/91

= [{1+(0.0165 x 183/365)} / [1+(0.0155 x 92/365)} - 1 ]x 365/91

= [1.00435 -1 ] x 365/91

= 0.01745 = 1.75%

So the value of contract 30 days from now = [(.01745 - 0.0166) x 91/365] x 100,000,000

= 21,191.78

Value of the FRA = 21191.78/[1+(0.0155 x 92/365)]

= 21,109.31 = $21,109

Please like the solution if satisfied and drop a comment in case of any doubts.

Thankyou