On consistent stochastic processes in the Nelson-Siegel framework

Abstract

The Nelson-Siegel model is used by many practitioners in the field of yield curve fitting and modeling. In the beginning it was just a method to fit the yield curve, nowadays people have developed methods using the Nelson-Siegel curve to predict the yield curve. This model, as a forecasting method based on continuous processes, lacks theoretical background. We take over Filipović’s the definition of the consistent state space process: the process which, when representing the parameters of the Nelson-Siegel curve, turns the discounted bond price into a martingale (what can be seen as the no-arbitrage condition). For Itô processes, it is shown there exists no nontrivial interest rate model consistent with the Nelson-Siegel family. Secondly we introduce jump processes and stochastic calculus for jump processes. We derive conditions on the dynamics of an Independent jump process in order to represent a consistent state space process. It turns out that there exists no nontrivial interest rate model driven by an Independent jump process.