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Multi-Lag Term Structure Models with Stochastic Risk Premia

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  • Alain Monfort

    (Crest)

  • Fulvio Pegoraro

    (Crest)

Abstract

In this paper we propose a family of discrete-time term structure models where we specify a Gaussian autoregressiveof order p > 1 historical and risk-neutral dynamics for the factor (xt), considered as a latent or observable variable: inthe second case the factor is a vector of several yields. We present the Gaussian AR(p) Factor-Based Term StructureModel in which the stochastic discount factor (SDF) for the period (t, t + 1) is specified as an exponential-affinefunction of xt+1, the factor risk-correction coefficient is stochastic, and the associated yield-to-maturity formulaat time t is an affine function of Xt = (xt, . . . , xt-p+1)0. We propose the Moving Average (or Heath, Jarrow andMorton) characterization of the yield and short-term forward rate processes, under the risk-neutral and the S-forwardprobability : this representation gives the possibility to exactly replicate the currently-observed yield curve. We alsostudy the problem of matching the theoretical and the currently-observed market term structure by means of theExtended AR(p) approach. We present the Gaussian VAR(p) Factor-Based Term Structure Model, generalizing thepreviously mentioned results to the multivariate framework.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2006-29.

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Length: 45
Date of creation: 2006
Date of revision:
Handle: RePEc:crs:wpaper:2006-29

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  1. 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.
  2. 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.
  3. 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.
  4. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 105-153.
  5. Pennacchi, George G, 1991. "Identifying the Dynamics of Real Interest Rates and Inflation: Evidence Using Survey Data," Review of Financial Studies, Society for Financial Studies, vol. 4(1), pages 53-86.
  6. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
  7. Christian Gourieroux & Alain Monfort & Vassilis Polimenis, 2005. "Affine Model for Credit Risk Analysis," Working Papers 2005-44, Centre de Recherche en Economie et Statistique.
  8. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
  9. 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.
  10. Andrew Ang & Monika Piazzesi & Min Wei, 2003. "What does the yield curve tell us about GDP growth?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  12. Christian Gourieroux & Alain Monfort & Vassilis Polimenis, 2002. "Affine Term Structure Models," Working Papers 2002-49, Centre de Recherche en Economie et Statistique.
  13. 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.
  14. 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.
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Cited by:
  1. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2007. "Econometric Asset Pricing Modelling," Working Papers 2007-18, Centre de Recherche en Economie et Statistique.
  2. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models - Extended Version," Working Papers 2007-19, Centre de Recherche en Economie et Statistique.
  3. Monfort, A. & Renne, J-P., 2011. "Default, liquidity and crises: an econometric framework," Working papers 340, Banque de France.

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