Question

Suppose that a party wanted to enter into an FRA that expires in 42 days and is based on 137-day LIBOR. The dealer quotes a rate of 4.75% on this FRA. Assume that at expiration, the 137-day LIBOR is 4% and the notional principal is $40,000,000.

Calculate the FRA payoff on a short position .

Answer 1

Solution:-

FRA Expiry = 42 days

FRA contract period(period between settlement and expiry date) = 137 days

No. of days in a year = 360 days

137 day LIBOR rate = 4%

Fixed rate = 4.75%

Notional price = $40,000,000

A short period in an FRA receives fixed and pays floating(LIBOR)

FRA Savings = (4.75%-4%) * 40,000,000 *(137/360)

= 0.75% * 40,000,000 * 0.3805

= $114,150

FRA pay off = PV of FRA savings on settlement date = 114,150 / 1+(0.04 * 137/360)

= 114,150 / 1+0.152

= 114,150 / 1.0152

= $112,440.89

Hence the FRA pay off on short position is $112,440.89