On Swap Rate Dynamics: To Freeze or Not to Freeze?

International Journal of Computer Mathematics, 94:11, 2208-2222

16 Pages Posted: 22 Oct 2015 Last revised: 8 Jul 2020

See all articles by Raquel M. Gaspar

Raquel M. Gaspar

ISEG and Cemapre/REM, Universidade de Lisboa

Rita Pimentel

University of Lisbon - CEMAT

Date Written: 2017

Abstract

We explore the implications of a common market and academic practice which is known as freezing the drift when dealing with swap interest rate dynamics.

In mathematical terms this can be better understood as imposing a low variance martingale (LVM) assumption. We look into the LVM Assumption implications, both on the shape and dynamics for default-free yield curves. We show that the LVM Assumption is equivalent to consider future yield curves are nothing but deterministic translations of the initial curve. For the particular case of the Nelson Siegel yield curve calibration, we show the LVM Assumption requires a deterministic parameter's evolution and, thus, imposes the need to constantly recalibrate the model.

Finally, based upon ECB historical data on evolution of the default-free Euro area yield curve, we illustrate periods in which the LVM may be applicable and others in which is not.

Keywords: drift freeze, low variance martingale, instantaneous forward rate, yield curve

JEL Classification: E43, G13

Suggested Citation

Gaspar, Raquel M. and Pimentel, Rita, On Swap Rate Dynamics: To Freeze or Not to Freeze? (2017). International Journal of Computer Mathematics, 94:11, 2208-2222, Available at SSRN: https://ssrn.com/abstract=2677709 or http://dx.doi.org/10.2139/ssrn.2677709

Raquel M. Gaspar

ISEG and Cemapre/REM, Universidade de Lisboa ( email )

Rua Miguel Lupi, 20
room 510
Lisbon, 1249-078
Portugal

Rita Pimentel (Contact Author)

University of Lisbon - CEMAT ( email )

Lisboa, 1749-016
Portugal

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