# Relationship between simple Libor spot and forward rates

How is the simple forward rate L(0,T,T+1) calculated given the spot rate L(0,T)?

• You cant calculate a forward rate from a single LIBOR spot rate unless you make some (strong) assumptions Jul 2, 2022 at 10:06
• Thanks, sure, but how do you derive the forward rate(s) if i have 12x monthly spot rates?
– user62731
Jul 2, 2022 at 11:01

USD Libor rates are quoted on a Act/360 basis. You can determine USD Libor forward rates by application of the following formula.

$$(1 + \text{SpotRate}(t) \times (\text{Act}(0,t)/360)) \times (1 + \text{FrdRate}(t,T) \times (\text{Act}(t,T)/360)) = (1 + \text{SpotRate}(T) \times (\text{Act}(0,T)/360)$$

where:

SpotRate(t) = the short term spot rate;

SpotRate(T) = the long term sport rate;

FrdRate(t,T) = forward rate from t to T;

Act(0,t) = Actual days from 0 to t;

Act(0,T) = Actual days from 0 to T;

Act(t,T) = Actual days from t to T

Note: This is for USD Libor and most other currency Libor rates. However, some currencies, such as GBP Libor are quoted on a 365 day basis. For these currencies you would substitute 365 for 360. Be sure to make sure you are using the appropriate daycount convention for the currency.