20. 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.
21. You have entered into the 69 FRA of Question 20 at the rate of 6%. After three months,
the FRA is now a 3 °ø 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.
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20. To calculate the payoff of the FRA, we need to determine the difference between the actual three-month Libor rate and the contracted rate.
The contracted rate is 6%.
The actual three-month Libor rate is 6.6% over 91 days.
The payment is made right away, so the actual period is 91/360.
The FRA payoff can be calculated as follows:
Payoff = Notional Amount × (Actual Libor Rate - Contracted Rate) × (Actual period/Actual year)
Payoff = 6,000,000 × (0.066 - 0.06) × (91/360) = $18,000
Therefore, the payoff of the FRA is $18,000.
21. To calculate the current value of the FRA, we need to determine the present value of the difference between the contracted rate and the expected three-month Libor rate.
The contracted rate is 6%.
The expected three-month Libor rate is 5% over 92 days.
The actual period is 92/360.
The present value of the FRA can be calculated as follows:
Present Value = Notional Amount × (Expected Libor Rate - Contracted Rate) × (Actual Period/Actual Year) × (1/(1 + Expected Libor Rate × (Actual Year/Actual Period)))
Present Value = 6,000,000 × (0.05 - 0.06) × (92/360) × (1/(1 + 0.05 × (360/92))) = -$13,920.96
Therefore, the current value of the FRA is -$13,920.96.
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