Arbitrage-Free Nelson-Siegel

This chapter discusses a new class of affine arbitrage-free models that overcome the problems with empirical implementation of the canonical affine arbitrage-free model. This new class is based on the dynamic Nelson–Siegel model (DNS) and retains its empirical tractability. Thus, from one perspective, the chapter takes the theoretically rigorous but empirically problematic affine arbitrage-free model and makes it empirically tractable by incorporating DNS elements. From an alternative perspective, it takes the DNS model and makes it theoretically more satisfactory. DNS is simple and stable to estimate, and it is quite flexible and fits both the cross section and time series of yields remarkably well. However, DNS fails on an important theoretical dimension: It does not impose the restrictions necessary to eliminate opportunities for riskless arbitrage. The lack of freedom from arbitrage motivated Diebold et al. (2005) and Christensen et al. (2011) to introduce the class of arbitrage-free Nelson–Siegel (AFNS) yield curve models, which are affine arbitrage-free term structure models that nevertheless maintain the DNS factor-loading structure.