CCAR-Consistent Yield Curve Stress Testing: From Nelson-Siegel to Machine Learning

Abstract

Following the financial crisis of 2008, the regulators established a stress testing framework known as comprehensive capital analysis and review (CCAR). The regulatory stress scenarios are macroeconomic and do not define stress values for all the relevant risk factors. In particular, only three Treasury rates are captured in these scenarios - 3-month, 5-year, and 10-year ones. Banks that are subject to CCAR, need to complement CCAR scenarios by defining stress values for the missing risk factors. The Treasury rates corresponding to different nodes are highly correlated. Hence, the changes in the three Treasury rates defined in the regulatory scenarios should somehow impact the other rates. In this paper, we will focus on the CCAR-consistent Treasury yield curve stress testing. We will consider three modeling approaches that would allow one to "build" the stressed curves under CCAR scenarios. We will start with the Nelson-Siegel (NS) approach, a well know yield curve smoothing technique. We will show how to convert the changes in the three Treasury rates to the changes in the NS parameters in order to "build" a stressed curve. We will then review a more common approach, namely, principal component analysis (PCA). PCA approach fits scenario generation problem better because it explicitly takes into consideration correlation between historical changes in rates corresponding to different nodes. In the case of PCA, we will demonstrate how to convert the changes in the three Treasury rates to the changes in the principal components. Finally, we will review the artificial neural network (ANN) approach, a well known machine learning technique. This approach will allow us to directly link the changes in the three Treasury rates to the changes in the other rates. The performance of these approaches will be assessed via back-testing.

Keywords: Machine Learning, Artificial Neural Networks (ANN), Principal Component Analysis (PCA), Nelson-Siegel (NS), Yield Curve, Curve Dynamics, Stress Testing, Comprehensive Capital Analysis and Review

JEL Classification: C61, C63, C53, C45