Mary Hames has bought a long FRAwith a notional principal of $10 million. The agreement expires in 30 days, and is based on 90-day LIBOR. The FRA is based upon an initial rate of 4.75%. Assume that at expiration, 90-day LIBOR is 5.5%, and 60-day LIBOR is 5.25%. Calculate the payoff at expiration.
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A. B. C.B
To calculate the payoff at expiration for the long FRA, we need to determine the difference between the actual 90-day LIBOR rate at expiration and the fixed rate agreed upon at the start of the FRA.
Given information:
First, let's determine the implied 30-day LIBOR rate at expiration using the 60-day and 90-day rates. We can assume a linear interpolation to estimate this rate:
30-day LIBOR = (90-day LIBOR - 60-day LIBOR) * (30/90) + 60-day LIBOR = (5.5% - 5.25%) * (30/90) + 5.25% = 0.25% * (30/90) + 5.25% = 0.0833% + 5.25% = 5.3333%
Next, we calculate the difference between the 90-day LIBOR rate at expiration and the fixed rate agreed upon at the start of the FRA:
Payoff = (90-day LIBOR at expiration - Fixed rate) * (Notional principal) * (Days/360) = (5.5% - 4.75%) * $10,000,000 * (30/360) = 0.75% * $10,000,000 * (30/360) = $75,000
Therefore, the payoff at expiration is $75,000. Since the question asks for the amount paid to Mary Hames, the correct answer is not provided among the options.