Improved scalability and risk factor proxying with a two-step principal component analysis for multi-curve modelling

We consider the practice-relevant problem of modelling multiple price curves to support activities such as price curve simulation and risk management. In this multi-curve setting, the challenge is to jointly capture the risk-factor relationships within each curve and the risk-factor relationships between the curves. Contributing to the existing literature, we develop a novel two-step Principal Component Analysis (PCA) method, which we label PCA², that addresses this challenge. The concept of PCA² first derives components describing the dynamics of each curve, and then, second, combines these to describe the dynamics across all the curves. The benefits of PCA² over PCA are: (i) improved scalability allowing for greater computational efficiency and smaller data structures rendering multi-threading more feasible; (ii) components that remain identifiable at the curve level; and (iii) leveraging the last property, PCA², unlike PCA, offers the capability of proxying new curves for which limited historical data exists, using the first-step components from a related curve and estimating second-level correlations empirically. PCA² is a novel multi-curve modelling approach that will appeal, for these reasons, to many practitioners, especially those working in risk management.