Nonlinear Kalman Filtering in Affine Term Structure Models
AbstractWhen the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi?ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze the potential of the unscented Kalman ?filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman ?filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive Monte Carlo experiment demonstrates that the unscented Kalman fi?lter is much more accurate than its extended counterpart in fi?ltering the states and forecasting swap rates and caps. Our fi?ndings suggest that the unscented Kalman fi?lter may prove to be a good approach for a number of other problems in fi?xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-49.
Date of creation: 14 May 2012
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Web page: http://www.econ.au.dk/afn/
Kalman filtering; nonlinearity; term structure models; swaps; caps.;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-06 (All new papers)
- NEP-CMP-2012-12-06 (Computational Economics)
- NEP-ECM-2012-12-06 (Econometrics)
- NEP-ETS-2012-12-06 (Econometric Time Series)
- NEP-FOR-2012-12-06 (Forecasting)
- NEP-ORE-2012-12-06 (Operations Research)
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