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# A Semi-Parametric Factor Model for Interest Rates

## Author Info

Listed author(s):
• Eric Ghysels
• Serena Ng
Registered author(s):

## Abstract

Understanding the dynamics of interest rates and the term structure has important implications for issues as diverse as real economic activity, monetary policy, pricing of interest rate derivative securities and public debt financing. Our paper follows a longstanding tradition of using factor models of interest rates but proposes a semi-parametric procedure to model interest rates. In a semi-parametric approach one typically parameterizes the object of interest while leaving unspecified the rest of the model. We construct factors as linear functionals of key economic time series involving unknown parameters, but treat the response of interest rates to the factors in a nonparametric way. The Average Derivating Estimator, which is a semi-parametric procedure proposed by Hardle and Stoker (1989) and Powell, Stock and Stoker (1989), allows us to proceed in two steps, namely we first identify factors without assuming knowledge of the response function of interest rates to the factors. Once the factors are identified, we proceed with estimating the response function using nonparametric methods. We can view our semi-parametric approach as a prelude to a fullblown parametric formulation for a factor term structure model. Indeed, our empirical results suggest a short term rate specification which deviates from standard parametric models often considered in the literature. Dans cette étude nous proposons des modèles à facteurs semi-paramétriques pour taux d'intérêts. Nous construisons les facteurs comme des fonctions linéaires de variables clés normales et réelles. L'estimateur de dérivée moyenne, proposé par Hardle et Stoker (1989) et Powell, Stock et Stoker (1989) nous permet d'estimer ces facteurs comme fonctions linéaires sans connaître leurs relations avec les taux d'intérêts. Une fois les facteurs identifiés et estimés nous estimons dans une deuxième étape cette dernière relation par méthodes non-paramétriques.

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File URL: http://www.cirano.qc.ca/files/publications/96s-18.pdf

## Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 96s-18.

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 Length: 30 pages Date of creation: 01 Jul 1996 Handle: RePEc:cir:cirwor:96s-18 Contact details of provider: Postal: 1130 rue Sherbrooke Ouest, suite 1400, Montréal, Quéc, H3A 2M8Phone: (514) 985-4000Fax: (514) 985-4039Web page: http://www.cirano.qc.ca/Email: More information through EDIRC

## References

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1. Hubbard, R Glenn & Kashyap, Anil K, 1992. "Internal Net Worth and the Investment Process: An Application to U.S. Agriculture," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 506-534, June.
2. Singh, Radhey S. & Ullah, Aman, 1985. "Nonparametric Time-Series Estimation of Joint DGP, Conditional DGP, and Vector Autoregression," Econometric Theory, Cambridge University Press, vol. 1(01), pages 27-52, April.
3. Bansal, Ravi & Viswanathan, S, 1993. " No Arbitrage and Arbitrage Pricing: A New Approach," Journal of Finance, American Finance Association, vol. 48(4), pages 1231-1262, September.
4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
5. Powell, James L. & Stoker, Thomas M., 1992. "Optimal bandwidth choice for density-weighted averages," Working papers 3424-92., Massachusetts Institute of Technology (MIT), Sloan School of Management.
6. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
7. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
8. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
10. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
11. Robert J. Shiller & J. Huston McCulloch, 1987. "The Term Structure of Interest Rates," NBER Working Papers 2341, National Bureau of Economic Research, Inc.
12. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
13. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
14. Haerdle,Wolfgang & Stoker,Thomas, 1987. "Investigations smooth multiple regression by the method of average derivatives," Discussion Paper Serie A 107, University of Bonn, Germany.
15. Stambaugh, Robert F., 1988. "The information in forward rates : Implications for models of the term structure," Journal of Financial Economics, Elsevier, vol. 21(1), pages 41-70, May.
16. Courtadon, Georges, 1982. "The Pricing of Options on Default-Free Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 75-100, March.
17. Gouriéroux, Christian & Scaillet, O., 1994. "Estimation of the term structure from bond data," CEPREMAP Working Papers (Couverture Orange) 9415, CEPREMAP.
18. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
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