Dynamic Refinement of the Term Structure - Time Homogenous Term Structure Modeling

28 Pages Posted: 29 Dec 2016 Last revised: 6 Mar 2017

See all articles by Christian P. Fries

Christian P. Fries

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics; DZ Bank AG

Date Written: December 12, 2016

Abstract

In this note we consider a classical term structure model framework, that is, a HJM framework on a time-discrete tenor, like the LIBOR market model, using a sequence of tenor discretization, where the tenors are valid for a specific simulation time interval.

The setup then allows to model dynamic refinements of the tenor structure and, as a special case, a quasi time-homogenous tenor structure.

A time-homogenous tenor structure has some relevance in exposure simulations, where two requirements come together: it is desirable to model a finer tenor structure on the short end of the rate curve compared to the long end of the rate curve and, this property should persist in the simulation at a future time.

The property is easily fulfilled by models, which uses an equally fine discretization at all times, e.g., a short rate model, where simulation time discretization and tenor time discretization coincide.

As we will demonstrate, a refinement of the tenor structure via a simple interpolation of forward rates would either introduce a strong restriction on the model's volatility structure (as it is the case for a classical fixed tenor LIBOR market model) or introduce an arbitrage violation. The challenge in the refinement is to simulate the right stochastic drifts. Under a (milder) condition on the model's volatility structure, the drifts can be reconstructed using a single additional state variable. The additional state variable is only needed on the coarse discretization tenors, limiting the computational resources needed to implement the model.

In a limit case, the approach can be used to glue together a short rate model for the short end of the rate curve and a term-structure model for the long end of the rate curve in a time-homogenous way.

Keywords: LIBOR Market Model, Heath-Jarrow-Morton Framework, Tenor Discretization, Term-Structure Models

JEL Classification: C15, G13

Suggested Citation

Fries, Christian P., Dynamic Refinement of the Term Structure - Time Homogenous Term Structure Modeling (December 12, 2016). Available at SSRN: https://ssrn.com/abstract=2884699 or http://dx.doi.org/10.2139/ssrn.2884699

Christian P. Fries (Contact Author)

Ludwig Maximilian University of Munich (LMU) - Faculty of Mathematics ( email )

Theresienstrasse 39
Munich
Germany

DZ Bank AG ( email )

60265 Frankfurt am Main
Germany

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