Arbitrage Smoothing in Fitting a Sequence of Yield Curves

Empirical modeling of the yield curve is often inconsistent with absence of arbitrage. In fact, many parsimonious models, like the popular Nelson-Siegel model, are inconsistent with absence of arbitrage. In other cases, arbitrage-free models are often used in inconsistent ways by recalibrating parameters that are assumed constant. For these cases, this paper introduces an arbitrage smoothing device to control arbitrage errors that arise in fitting a sequence of yield curves. The device is applied to the US term structure for the family of Nelson-Siegel curves. It is shown that the arbitrage smoothing device contributes to parameter stability and smoothness