Valuation of Arithmetic Average of Fed Funds Rates and Construction of the US Dollar Swap Yield Curve

Abstract

Arithmetic averages of Fed Funds (FF) rates are paid on the FF leg of a FF-LIBOR basis swap, while the FF rates are paid with daily compounding in an Overnight Index Swap. We consider here how to value the arithmetic average of FF rates and calculate convexity adjustment terms relative to daily compounded FF rates. FF-LIBOR basis swaps are now the critical calibration instruments for traders to construct the US dollar swap yield curve. We also show how it is constructed in practice.

Keywords: OIS Discounting, Federal Funds Rate, Overnight Rate, Convexity Adjustment, Yield Curve, Arithmetic Average, FF-LIBOR Basis Swap, Collateralized Swap, Risk Neutral Valuation, Hull White Model, Cap and Floor

JEL Classification: G13