ACT/360 Convention You have entered into the 69 FRA of Question 20 at the rate of 6%. After three months, the FRA is now a 3 × 6 FRA. If the three-month Libor rate is 5%, and the six-month Libor rate is 7%, what is the current value of the FRA? Assume that the number of days in the first three months is 92. 20.
ACT/360 Convention You enter into an FRA of notional 6 million to borrow on the three-month underlying Libor rate six months from now and lock in the rate of 6%. At the end of six months, if the underlying three-month rate is 6.6% over an actual period of 91 days, what is your payoff given that the payment is made right away? Recall that the ACT/360 convention applies. The payoff for the FRA is $9,073.92 and the current value of the FRA is $306,720. 21. In this case, the original FRA of a notional 6 million has transformed into a 3 × 6 FRA after three months. The 3 × 6 FRA implies a three-month borrowing period starting three months from now and ending six months from now.
To calculate the current value of the FRA, we need to compare the locked-in rate of 6% with the current market rates for the corresponding periods. The three-month Libor rate is 5% and the six-month Libor rate is 7%. Using the ACT/360 convention, the locked-in rate of 6% per annum corresponds to a 0.5% rate for three months. The current three-month Libor rate of 5% corresponds to a 0.4167% rate for three months, and the six-month Libor rate of 7% corresponds to a 0.5833% rate for three months. ACT/360 Convention To calculate the value of the FRA, we take the difference between the locked-in rate and the current market rate for the relevant period. In this case, it would be 0.5% – 0.4167% = 0.0833% Multiplying this by the notional amount of 6 million gives us the current value of the FRA: 0.0833% * 6,000,000 = 4,999.8. Therefore, the current value of the FRA is approximately 4,999.8. Overall, your payoff in scenario 20 would be 3,000, while the current value of the FRA in scenario 21 is approximately 4,999.8. Use APA referencing style.