The forward rate is the future yield on a bond. It is calculated using the yield curve. For example, the yield on a three-month Treasury bill six months from now is a forward rate.

Forward rate calculation

To extract the forward rate, we need the zero-coupon yield curve.

We are trying to find the future interest expressed in years. To do this, we use the property, following from the arbitrage-free pricing of bonds and then reinvesting.

depends on the rate calculation mode (simple, yearly compounded or continuously compounded), which yields three different results.

Mathematically it reads as follows:

Simple rate

yields:

Yearly compounded rate

yields :

The discount factor formula for period (0,t, the forward rate can be expressed in terms of discount factors:

Continuously compounded rate

yields:

1. STEP 1→

   STEP 2→

   STEP 3→

   STEP 4→

   STEP 5→

The discount factor formula for period (0,t, the forward rate can be expressed in terms of discount factors:

.

, (k = 1,2).

Related instruments

• Forward rate agreement

• Floating rate note

See also

• Forward price

• Spot rate

References