Reproducing kernel Hilbert space methods for modelling the discount curve

TL;DR

This paper introduces reproducing kernel Hilbert space methods for modeling the discount curve, providing a tractable approach for calibration in the HJM framework with real-world treasury data.

Contribution

It develops a novel kernel-based regression method for estimating admissible discount curves under no-arbitrage conditions in the HJM model.

Findings

Kernel methods effectively calibrate discount curves from market data.

Polynomial and exponential functions characterize admissible discount curves.

Numerical analysis demonstrates practical applicability with treasury data.

Abstract

We consider the theory of bond discounts, defined as the difference between the terminal payoff of the contract and its current price. Working in the setting of finite-dimensional realizations in the HJM framework, under suitable notions of no-arbitrage, the admissible discount curves take the form of polynomial, exponential functions. We introduce reproducing kernels that are admissible under no-arbitrage as a tractable regression basis for the estimation problem in calibrating the model to market data. We provide a thorough numerical analysis using real-world treasury data.