Question

Given a FRA with the following terms:

• Notional principal = $20 million
• Reference rate = LIBOR
• Contract rate = R_k = 2.00% (annual)
• Time period = 90 days
• Day-count convention = Actual/365

Show in a table the payments and receipts for long and short positions on the FRA given possible spot LIBORs at the FRA’s expiration of 1.00%, 1.50%, 2.00%, 2.50%, and 3.00%. Show your work.

Answer 1

long position

at rate 1% gain = 20,000,000 * 90/365 * (1 - 2)% = -49,315.07

at rate 1.5% gain = 20,000,000 * 90/365 * (1.5 - 2)% = -24,657.53

at rate 2% gain = 20,000,000 * 90/365 * (2 - 2)% = 0

at rate 2.5% gain = 20,000,000 * 90/365 * (2.5 - 2)% = 24,657.53

at rate 3% gain = 20,000,000 * 90/365 * (3 - 2)% = 49,315.07

short position will only be the reverse of the long position since it is a zero sum gain