A Heat Kernel Approach to Interest Rate Models

TL;DR

This paper introduces a novel interest rate modeling approach using heat kernels, emphasizing analytical tractability and generality through the propagation property within the state price density framework.

Contribution

It presents a new heat kernel-based method for constructing interest rate models that are analytically tractable and broadly applicable, extending existing state price density approaches.

Findings

Heat kernels possess a propagation property useful for interest rate modeling.

The proposed approach enhances analytical tractability of interest rate models.

The method generalizes existing models by leveraging heat kernel properties.

Abstract

We construct default-free interest rate models in the spirit of the well-known Markov funcional models: our focus is analytic tractability of the models and generality of the approach. We work in the setting of state price densities and construct models by means of the so called propagation property. The propagation property can be found implicitly in all of the popular state price density approaches, in particular heat kernels share the propagation property (wherefrom we deduced the name of the approach). As a related matter, an interesting property of heat kernels is presented, too.