Arbitrage-free Nelson–Siegel model for multiple yield curves

We propose an affine term structure model that allows for tenor-dependence of yield curves and thus for different risk categories in interbank rates, an important feature of post-crisis interest rate markets. The model has a Nelson–Siegel factor loading structure and thus economically well interpretable parameters. We show that the model is tractable in terms of estimation and provides good in-sample fit and out-of-sample forecasting performance. The proposed model is arbitrage-free across maturities and tenors, and thus perfectly suited for risk management and pricing purposes. We apply our framework to the pricing of caplets in order to illustrate its practical applicability and its suitability for stress testing.

Impact of Foreign Official Purchases of US Treasuries on the Yield Curve

Foreign governments went from owning a tenth of publicly available US Treasury notes and bonds in 1985 to over half in 2008. Recently, foreign governments have reduced their positions. I find foreign official purchases have depressed medium-term yields, despite conventional wisdom pointing toward the long end of the yield curve. To examine effects over the entire yield curve, I embed a structural vector autoregression of macroeconomic variables into an affine term structure model. With segments of the yield curve increasingly determined by international financial markets, it may be more difficult for the Federal Reserve to implement its interest rate policy.

Estimating the Term Structure with Linear Regressions: Getting to the Roots of the Problem

Linear estimators of the affine term structure model are inconsistent since they cannot reproduce the factors used in estimation. This is a serious handicap empirically, giving a worse fit than the conventional ML estimator that ensures consistency. We show that a simple self-consistent estimator can be constructed using the eigenvalue decomposition of a regression estimator. The remaining parameters of the model follow analytically. Estimates from this model are virtually indistinguishable from that of the ML estimator. We apply the method to estimate various models of U.S. Treasury yields. These exercises greatly extend the range of models that can be estimated.