A generalised arbitrage-free Nelson–Siegel model: The impact of unspanned stochastic volatility

Abstract

Although statistical term structure models provide exceptional in-sample fitting and out-of-sample forecasting of interest rates, the lack of theoretical background is criticized by academics and practitioners, such as the absent of arbitrage free. In this paper we develop a general Arbitrage-Free Nelson–Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson–Siegel factor loading structure. This paper also exploits the potential to jointly model the interest rates and their derivatives.