Nonlinear Filtering in Affine Term Structure Models: Evidence from the Term Structure of Swap Rates

56 Pages Posted: 18 Jun 2008 Last revised: 1 Aug 2009

See all articles by Peter Christoffersen

Peter Christoffersen

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

Kris Jacobs

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

Lotfi Karoui

Goldman, Sachs & Co

Karim Mimouni

McGill University - Desautels Faculty of Management

Date Written: July 20, 2009

Abstract

When the relationship between observed fixed-income securities and the latent state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear filtering is computationally demanding. We propose the use of the unscented Kalman filter to allow for nonlinearities. To illustrate its advantages, we analyze the cross section of swap rates, which are relatively simple nonlinear instruments. An extensive Monte Carlo experiment demonstrates that the unscented Kalman filter generates much smaller swap rate prediction errors and also smaller errors in parameter estimates. Estimation using swap data indicates large differences between the state variables obtained using the unscented Kalman filter and the more conventional extended Kalman filter. Our findings suggest that the unscented Kalman filter may prove to be a good approach for a number of other problems in fixed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using interest rate derivatives or coupon bonds, and the estimation of quadratic term structure models.

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

JEL Classification: G12

Suggested Citation

Christoffersen, Peter and Jacobs, Kris and Karoui, Lotfi and Mimouni, Karim, Nonlinear Filtering in Affine Term Structure Models: Evidence from the Term Structure of Swap Rates (July 20, 2009). Available at SSRN: https://ssrn.com/abstract=1147343 or http://dx.doi.org/10.2139/ssrn.1147343

Peter Christoffersen (Contact Author)

University of Toronto - Rotman School of Management ( email )

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

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

Kris Jacobs

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

Karim Mimouni

McGill University - Desautels Faculty of Management ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1
Canada

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