Backward
Subtype of LookingThe backward looking term rate R becomes known at the end Tₙ of the calculation period [T₀,Tₙ]
This is the conceptually easiest definition of the term rate as it allows its determination based solely on the by the time Tₙ already observed values I₀, I₁,..., Iₙ on the dates T₀, T₁,..., Tₙ of the referenced overnight index I.
Note, R is not known prior to time Tₙ
When viewed from a time earlier than T₀, both backward and Forward looking rates are random variables with the same mean, but different variances.
It follows that backwardness or forwardness has no impact on the price of payoffs that depend linearly on term rates whose calculation period lies in the future, but do so on all other cases.
Therefore, the price of a spot starting OIS would not depend on how its term rate is defined, whereas that of a past starting OIS, of which the earliest forthcoming cash flow has a calculation period that starts in the past, would do so.
Also the prices of caps and swaptions referencing overnight index term rates would depend on how their term rates are defined.
More precisely, due to higher variances associated with backward looking as compared with forward looking term rates, the caps and swaptions on the former will be more expensive than those on the latter.