Improved scalability and risk factor proxying with a two-step principal component analysis for multi-curve modelling
提出一种两步主成分分析法（PCA2），先提取单曲线动态成分再跨曲线组合，相比传统PCA提升了计算效率、曲线级可识别性，并能用相关曲线数据代理历史数据不足的新曲线，对风险管理从业者尤其有用。
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.