An Arbitrage-Free Nelson-Siegel Model with Unspanned Stochastic Volatility for the Pricing of Interest Rate Derivatives

Abstract

We propose a generalized arbitrage-free Nelson-Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson-Siegel factor loading structure. The price of the interest rate derivatives, including European options, Caps and Swaptions are then obtained in semi closed-form. We calibrate the model using an extensive panel data, including the US Libor rates, Swap rates, caps and swaptions. By estimating our model via the extended Kalman filter, we find strong evidence that our model prices interest rates and their derivatives accurately.