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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.

Suggested Citation

  • Alain Monfort & Fulvio Pegoraro, 2006. "Multi-Lag Term Structure Models with Stochastic Risk Premia," Working Papers 2006-29, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2006-29
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
    5. Christian Gourieroux & Alain Monfort & Vassilis Polimenis, 2002. "Affine Term Structure Models," Working Papers 2002-49, Center for Research in Economics and Statistics.
    6. 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, February.
    7. Alain Monfort & Fulvio Pegoraro, 2007. "Switching VARMA Term Structure Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 105-153.
    8. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    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.
    10. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    11. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    12. C. Gourieroux & A. Monfort & V. Polimenis, 2006. "Affine Models for Credit Risk Analysis," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 494-530.
    13. 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.
    14. 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 1011-1029, December.
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    Cited by:

    1. Monfort, A. & Pegoraro, F., 2007. "Switching VARMA Term Structure Models - Extended Version," Working papers 191, Banque de France.
    2. H. Bertholon & A. Monfort & F. Pegoraro, 2008. "Econometric Asset Pricing Modelling," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(4), pages 407-458, Fall.
    3. Alain Monfort & Jean-Paul Renne, 2013. "Default, Liquidity, and Crises: an Econometric Framework," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(2), pages 221-262, March.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G1 - Financial Economics - - General Financial Markets

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