The typically observed upward sloping nominal yield curve implies that investors demand positive risk premia -or term premia -to hold long-term nominal bonds. Fundamentally, the term premium is compensation to investors for bearing interest rate risk and a component in the term structure of yields. There is substantial evidence of sizeable and time-varying term premia. As opposed to yields, term premia are not directly observable. In this paper we estimate term premia in Norwegian government bond yields from a set of dynamic term structure models (DTSM), covering the period from 2003/01 until 2021/04. In line with international studies, we find evidence of declining term premia over the sample period.

In this study we propose a semi-parametric, parsimonious Value at Risk forecasting model, based on quantile regression and machine learning methods, combined with readily available market prices of option contracts from the over-the-counter foreign exchange rate interbank market. We aim at improving existing methods for VaR prediction of currency investments using machine learning. We employ two different methods - ensemble methods and neural networks. Explanatory variables are implied volatilities with plausible economic interpretation. The forward-looking nature of the model, achieved by the application of implied volatilities as risk factors, ensures that new information is rapidly reflected in Value at Risk estimates. To the best of our knowledge, this paper is the first to utilize information in the volatility surface, combined with machine learning and quantile regression, for VaR prediction of currency investments. The proposed ensemble models achieve good estimates across all quantiles. The light gra-dient-boosting machine model and the categorical boosting model both yield estimates which are better than, or equal to, those of the benchmark model. The neural network models are in general quite unstable.

Principal component analysis (PCA) is well established as a powerful statistical technique in the realm of yield curve modeling. PCA based term structure models typically provide accurate fit to observed yields and explain most of the cross-sectional variation of yields. Although principal components are building blocks of modern term structure models, the approach has been less explored for the purpose of risk modelling—such as Value-at-Risk and Expected Shortfall. Interest rate risk models are generally challenging to specify and estimate, due to the regime switching behavior of yields and yield volatilities. In this paper, we contribute to the literature by combining estimates of conditional principal component volatilities in a quantile regression (QREG) framework to infer distributional yield estimates. The proposed PCA-QREG model offers predictions that are of high accuracy for most maturities while retaining simplicity in application and interpretability.

Fundamentally, the term premium in long-term nominal yields is compensation to investors for bearing interest rate risk. There is substantial evidence of sizable and time-varying term premia. As opposed to yields, term premia are not directly observable. In this paper, we estimate term premia in Norwegian interest rate swaps from a set of dynamic term structure models, covering the period from 2001/04 until 2022/06. In line with international studies, we find evidence of declining term premia over the sample period. Furthermore, our estimates indicate that term premia have been close to zero, as well as negative in periods, during the last decade of global extraordinary monetary policy measures. We find that the recent rise in Norwegian interest rate swaps is partly caused by increases in term premia. From a practitioner’s perspective, our term premia estimates can be utilized as part of applied management of both investment and debt portfolios.