Factor Models and the Shape of the Term Structure

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Factor Models and the Shape of the Term Structure

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Schloegl, Erik, and Daniel Sommer

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Erik Schlogl

Abstract

he present paper analyses a broad range of one- and multifactor models of the term structure of interest rates. We assess the influence of the number of factors, mean reversion, and the factor probability distributions on the term structure shapes the models generate, and use spread options as an aggregate measure of the relative importance assigned to rising and falling forward rate curves by the models considered. We derive valuation formulas for these contingent claims in the multifactor Gaussian and CIR-models. Our main result is that the specification of mean reversion and the number of factors are both much more important for the relative movements of interest rates than the distributional characteristics of the factors. To the extent that interest rate risk depends on the movements of different parts of the term structure relative to one another rather than on shifts of its absolute level, the distributional assumption on the factor dynamics is found to be essentially irrelevant.

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Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 395.

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Date of creation: Jan 1997
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Handle: RePEc:bon:bonsfb:395

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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

Hugh Cohen & David Heath, 1992. "A new method of testing pricing models as applied to forward interest rate models," Working Paper 92-16, Federal Reserve Bank of Atlanta.
Amin, Kaushik I. & Morton, Andrew J., 1994. "Implied volatility functions in arbitrage-free term structure models," Journal of Financial Economics, Elsevier, vol. 35(2), pages 141-180, April. [Downloadable!] (restricted)
Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
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. [Downloadable!] (restricted)
Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
Schlögl, Erik, and Daniel Sommer, 1994. "On Short Rate Processes and Their Implications for Term Structure Movements," Discussion Paper Serie B 293, University of Bonn, Germany. [Downloadable!]
Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December. [Downloadable!] (restricted)
Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 3(4), pages 573-92. [Downloadable!] (restricted)

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Jean-Philippe Bouchaud & Nicolas Sagna & Rama Cont & Nicole El-Karoui & Marc Potters, 1997. "Phenomenology of the interest rate curve," Science & Finance (CFM) working paper archive 500048, Science & Finance, Capital Fund Management. [Downloadable!]
Other versions:
- Jean-Philippe Bouchaud, Nicolas Sagna, Rama Cont, Nicole El-Karoui, Marc Potters, 1999. "Phenomenology of the interest rate curve," Applied Mathematical Finance, Taylor and Francis Journals, vol. 6(3), pages 209-232, September. [Downloadable!] (restricted)
Jean-Philippe BOUCHAUD & Rama CONT & Nicole EL KAROUI & Marc POTTERS & Nicolas SAGNA, 1997. "Phenomenology of the interest curve," Finance 9712009, EconWPA. [Downloadable!]

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