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Multi-Lag Term Structure Models with Stochastic Risk Premia

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Author Info
Monfort, A.
Pegoraro, F.

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Abstract

The purpose of this paper is to propose discrete-time term structure models where the historical dynamics of the factor (xt) is given, in the univariate case, by a Gaussian AR(p) process, and, in the multivariate case, by a Gaussian n-dimensional VAR(p) process. The factor (xt) is considered as a latent or an observable variable and, in the second case, (xt) is given by the short rate (in the scalar setting) or by a vector of several yields (in the multivariate setting). We consider an exponential-affine stochastic discount factor (SDF) with a stochastic factor risk correction coefficient defined, at time t, as an affine function of Xt = (xt, . . . , xt?p+1)0 and, consequently, the yield-to-maturity formula at time t is an affine function of the p most recent lagged values of xt+1. We study the Gaussian AR(p) and the Gaussian VAR(p) Factor-Based Term Structure Models. We investigate, under the risk-neutral and the S-forward probability, the Moving Average (or discrete-time Heath, Jarrow and Morton) representation of the yield and short-term forward rate processes. This representation gives the possibility to exactly replicate the currently-observed yield curve. We also study the problem of matching the theoretical and currently-observed market term structure by means of the Extended AR(p) approach.

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Publisher Info
Paper provided by Banque de France in its series Documents de Travail with number 189.

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Length: 47 pages
Date of creation: 2007
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Handle: RePEc:bfr:banfra:189

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Related research
Keywords: Discrete-time Affine Term Structure Models ; Stochastic Discount Factor; Gaussian VAR(p) processes ; Stochastic risk premia ; Moving Average or discrete-time HJM representations ; Exact Fitting of the currently-observed yield curve.;

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C5 - Mathematical and Quantitative Methods - - Econometric Modeling
G1 - Financial Economics - - General Financial Markets

References listed on IDEAS
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  1. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02. [Downloadable!] (restricted)
  2. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January. [Downloadable!] (restricted)
  3. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models," Journal of Financial Econometrics, Oxford University Press, vol. 5(1), pages 105-153. [Downloadable!] (restricted)
  4. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October. [Downloadable!] (restricted)
  5. 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)
  6. Pennacchi, George G, 1991. "Identifying the Dynamics of Real Interest Rates and Inflation: Evidence Using Survey Data," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 4(1), pages 53-86. [Downloadable!] (restricted)
  7. Ang, Andrew & Piazzesi, Monika, 2003. "A no-arbitrage vector autoregression of term structure dynamics with macroeconomic and latent variables," Journal of Monetary Economics, Elsevier, vol. 50(4), pages 745-787, May. [Downloadable!] (restricted)
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  8. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 17(2), pages 379-404. [Downloadable!] (restricted)
  9. Ang, Andrew & Piazzesi, Monika & Wei, Min, 2006. "What does the yield curve tell us about GDP growth?," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 359-403. [Downloadable!] (restricted)
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  10. 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)
  11. 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)
  12. C. Gourieroux & A. Monfort & V. Polimenis, 2006. "Affine Models for Credit Risk Analysis," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 494-530. [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.)

  1. Monfort, A. & Pegoraro, F., 2007. "Switching VARMA Term Structure Models - Extended Version," Documents de Travail 191, Banque de France. [Downloadable!]
    Other versions:
  2. Bertholon, H. & Monfort, A. & Pegoraro, F., 2008. "Econometric Asset Pricing Modelling," Documents de Travail 223, Banque de France. [Downloadable!]
    Other versions:
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