Forward Rate Agreement - Payoff Formula

Payoff Formula

The netted payment made at the effective date is as follows $mbox{Payment} = mbox{Notional Amount} * left( frac{(mbox{Reference Rate}-mbox{Fixed Rate}) * alpha }{ 1 + mbox{Reference Rate} * alpha } right) " src="http://upload.wikimedia.org/math/d/f/b/dfb4a1629068ee416a6fca8e7ae516b7.png" />

• The Fixed Rate is the rate at which the contract is agreed.
• The Reference Rate is typically Euribor or LIBOR.
• is the day count fraction, i.e. the portion of a year over which the rates are calculated, using the day count convention used in the money markets in the underlying currency. For EUR and USD this is generally the number of days divided by 360, for GBP it is the number of days divided by 365 days.
• The Fixed Rate and Reference Rate are rates that should accrue over a period starting on the effective date, and then paid at the end of the period (termination date). However, as the payment is already known at the beginning of the period, it is also paid at the beginning. This is why the discount factor is used in the denominator.