Nonlinear Kalman Filtering in Affine Term Structure Models

46 Pages Posted: 24 May 2012 Last revised: 4 Oct 2013

See all articles by Peter Christoffersen

Peter Christoffersen

University of Toronto - Rotman School of Management; Copenhagen Business School; Aarhus University - CREATES

Christian Dorion

HEC Montreal

Kris Jacobs

University of Houston - C.T. Bauer College of Business

Lotfi Karoui

Goldman, Sachs & Co

Date Written: October 1, 2013

Abstract

The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed income applications. We investigate if the unscented Kalman filter should be used to capture nonlinearities, and compare the performance of the Kalman filter to that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also performs well when compared to the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may prove to be a good approach for variety of problems in fixed income pricing.

The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2322760

Keywords: Kalman filtering, nonlinearity, term structure models, swaps, caps

JEL Classification: G12

Suggested Citation

Christoffersen, Peter and Dorion, Christian and Jacobs, Kris and Karoui, Lotfi, Nonlinear Kalman Filtering in Affine Term Structure Models (October 1, 2013). Available at SSRN: https://ssrn.com/abstract=2065624 or http://dx.doi.org/10.2139/ssrn.2065624

Peter Christoffersen

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5P 3C4
Canada
416-946-5511 (Phone)

HOME PAGE: http://www.christoffersen.com

Copenhagen Business School

Solbjerg Plads 3
Frederiksberg C, DK - 2000
Denmark

Aarhus University - CREATES

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Christian Dorion

HEC Montreal ( email )

3000, Chemin de la Côte-Sainte-Catherine
Montreal, Quebec H2X 2L3
Canada
5143401522 (Phone)
5143405632 (Fax)

HOME PAGE: http://neumann.hec.ca/pages/christian.dorion/

Kris Jacobs (Contact Author)

University of Houston - C.T. Bauer College of Business ( email )

Houston, TX 77204-6021
United States

Lotfi Karoui

Goldman, Sachs & Co ( email )

1 New York Plaza
New York, NY 10004
United States

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