Spectral term structure models

TL;DR

This paper investigates a stochastic evolution equation in probability measure space, establishing existence and uniqueness, and connects it to interest rate term structure models similar to Heath-Jarrow-Morton framework.

Contribution

It introduces a novel stochastic evolution equation approach to modeling interest rate term structures, extending the Heath-Jarrow-Morton framework.

Findings

Proves existence and uniqueness of solutions

Links stochastic evolution to interest rate models

Provides a new mathematical foundation for term structure modeling

Abstract

This note studies a certain stochastic evolution equation in the space of probability measures, including existence and uniqueness results. A solution of this equation gives rise, in a natural way, to an interest rate term structure model, in the same spirit as the Heath-Jarrow-Morton framework.