Transfer Learning Across Fixed-Income Product Classes

ArXiv ID: 2505.07676 “View on arXiv”

Authors: Nicolas Camenzind, Damir Filipovic

Abstract

We propose a framework for transfer learning of discount curves across different fixed-income product classes. Motivated by challenges in estimating discount curves from sparse or noisy data, we extend kernel ridge regression (KR) to a vector-valued setting, formulating a convex optimization problem in a vector-valued reproducing kernel Hilbert space (RKHS). Each component of the solution corresponds to the discount curve implied by a specific product class. We introduce an additional regularization term motivated by economic principles, promoting smoothness of spread curves between product classes, and show that it leads to a valid separable kernel structure. A main theoretical contribution is a decomposition of the vector-valued RKHS norm induced by separable kernels. We further provide a Gaussian process interpretation of vector-valued KR, enabling quantification of estimation uncertainty. Illustrative examples demonstrate that transfer learning significantly improves extrapolation performance and tightens confidence intervals compared to single-curve estimation.

Keywords: Kernel Ridge Regression, Vector-valued Reproducing Kernel Hilbert Space, Transfer Learning, Discount Curves, Convex Optimization, Fixed Income

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, featuring advanced theory like vector-valued RKHS, separable kernels, and Gaussian process interpretations, with extensive LaTeX derivations. While it includes illustrative examples and promises empirical studies, it lacks code, backtests, or statistical metrics, focusing more on theoretical formulation than implementation-heavy validation.

  flowchart TD
    A["Research Goal: Develop transfer learning<br>framework for discount curves across<br>fixed-income product classes"] --> B{"Data: <br>Historical market data for<br>multiple product classes"}
    B --> C["Methodology: <br>Vector-valued Kernel Ridge Regression"]
    C --> D["Formulation: <br>Convex optimization in vector-valued RKHS<br>with separable kernels"]
    D --> E["Computation: <br>Gaussian Process interpretation for<br>uncertainty quantification & confidence intervals"]
    E --> F["Outcome: <br>Transfer learning improves extrapolation &<br>tightens confidence intervals vs. single-curve"]
    F --> G["Key Contribution: <br>Theoretical decomposition of RKHS norm<br>+ economic regularization for spread smoothness"]