Multiple Yield Curve Modeling and Forecasting using Deep Learning

Abstract

This manuscript introduces deep learning models that simultaneously describe the dynamics of several yield curves. We aim to learn the dependence structure among the different yield curves induced by the globalization of financial markets and exploit it to produce more accurate forecasts. By combining the self-attention mechanism and nonparametric quantile regression, our model generates both point and interval forecasts of future yields. The architecture is designed to avoid quantile crossing issues affecting multiple quantile regression models. Numerical experiments conducted on two different datasets confirm the effectiveness of our approach. Finally, we explore potential extensions and enhancements by incorporating deep ensemble methods and transfer learning mechanisms.

Figures (6)

• Figure 1: Diagram of the feature processing components of the DeepYC model. A matrix of spot rates is processed by three FCN layers in a time-distributed manner, to derive the key, query and value matrices which are then input into a self-attention operation.
• Figure 2: Diagram of the output components of the DeepYC model. The matrix of features produced by the first part of the model are flattened into a vector and then dropout is applied. We add a categorical embedding to this vector, and, finally, then the best-estimate and quantile predictions are produced.
• Figure 3: MSE, MAE, and PICP obtained by the YC_ATT and NSS_VAR models in the different countries.
• Figure 4: PICP of the NSS_VAR, YC_ATT, and YC_ATT_DE models for different time-to-maturities.
• Figure 5: Boxplot of the out-of-sample MSE, MAE, PICP and MPIW of the different models on ten runs; the MSE values are multiplied $10^5$, the MAE values are multiplied by $10^2$.