Discrete-Time Arbitrage-Free Nelson-Siegel Term Structure Model and Application

Abstract

We characterize the discrete-time arbitrage-free Nelson-Siegel term structure model, prove the uniqueness of the solution for model identification, make specification analysis on its canonical form, and detail the MCMC estimation method with a fast and reliable prior extraction step. Using the model, we examine how the yield curves of U.S. and China react to exchange rate policy shocks from China in its gradual reform to a more flexible exchange rate regime. Model decomposition reveals that, in U.S. yield responses, changes in risk premia for medium- to long-term yields dominate changes in yield expectation for short- to medium-term yields. The results are helpful to diagnosing market sentiment and exchange rate risk pricing as China further internationalizes its currency.