Predicting interest rate distributions using PCA & quantile regression

Abstract

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.