Identifying Term Structure Volatility from the Libor-Swap Curve

Abstract

This paper proposes a new family of specification tests and applies them to affine term structure models of the LIBOR swap curve. Contrary to Dai and Singleton (2000), the tests show that affine models do a poor job modelling volatility at the short end of the term structure. Improving the volatility process does not require different models, rather it requires different econometrics. The paper distinguishes between two econometric procedures for identifying volatility. The cross-sectional approach backs out volatility from a cross-section of bond yields, and the time series approach imputes volatility from time series variation in yields. For an affine model, the volatility implied by the time series procedure passes the specification tests, while the cross-sectionally identified volatility does not.

Keywords: term structure models, affine models

JEL Classification: C52, G13