Stochastic Volatility in the Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models

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Abstract
Christensen, Diebold and Rudebusch (2007) derive the affine arbitrage-free class of dynamic Nelson-Siegel models and find that it performs well in terms of forecasting yields. However, that class of models is limited by the fact that it only allows for Gaussian factors with constant volatility. In this paper, we modify the above class of models to incorporate stochastic volatility factors while preserving as much of the Nelson-Siegel factor loading structure as possible. We introduce five new classes of affine arbitrage-free models. Limiting ourselves to the extended affine risk premium specification introduced in Cheridito, Filipovic and Kimmel (2007), we derive the maximally flexible specification of each class of models. We study the in-sample and out-of-sample properties of the most flexible specification for each class as well as those of the most parsimonious specification where the factors are independent. The results are compared to those reported by Christensen, Diebold and Rudebusch (2007) for the regular class of arbitrage-free dynamic Nelson-Siegel models with constant volatility. The ultimate goal is to find a class of models that preserves the ability to forecast yields at least on par with the Nelson-Siegel model while being able to also forecast yield volatility. This is important when it comes to pricing volatility sensitive products such as interest rate derivatives.

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