LIBOR Interpolation and the HJM Model

TL;DR

This paper extends LIBOR interpolation methods to models with jumps, providing a way to construct an infinite LIBOR term structure from finite tenor models and analyzing necessary moment conditions for the HJM framework.

Contribution

It introduces an extension of LIBOR interpolation to jump models and connects finite tenor LIBOR models with the HJM model for infinite term structures.

Findings

Extended interpolation method for jump models.

Established connection between LIBOR and HJM models.

Demonstrated necessity of exponential moment conditions.

Abstract

We follow the lines of Musiela and Rutkowski and extend their interpolation method to models with jumps. Together with an extension method for the tenor structure of a given LIBOR market model (LMM) we get an infinite LIBOR termstructure. Furthermore we present an argument why certain known exponential moment conditions on the HJM Model are necessary. The approach uses finite tenor LIBOR market models as approximation for the HJM model, then extends and interpolates the tenor structure, relating it to the HJM structure.