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Staying at zero with affine processes: An application to term structure modelling

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  • Monfort, Alain
  • Pegoraro, Fulvio
  • Renne, Jean-Paul
  • Roussellet, Guillaume

Abstract

We build an Affine Term Structure Model that provides non-negative yields at any maturity and that is able to accommodate a short-term rate that stays at the zero lower bound (ZLB) for extended periods of time while longer-term rates feature high volatilities. We introduce these features through a new univariate non-negative affine process called ARG-Zero, and its multivariate affine counterpart (VARG), entailing conditional distributions with zero-point masses. The affine property of this new class of processes implies both explicit bond pricing and quasi-explicit lift-off probability formulas. We provide an empirical application to Japanese Government Bond (JGB) yields, observed weekly from June 1995 to May 2014 with maturities from six months to ten years. Our four-factor specification is able to closely match yield levels and to capture conditional yield variances.

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  • Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
  • Handle: RePEc:eee:econom:v:201:y:2017:i:2:p:348-366
    DOI: 10.1016/j.jeconom.2017.08.013
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    5. Marcello Pericoli & Marco Taboga, 2015. "Understanding policy rates at the zero lower bound: insights from a Bayesian shadow rate model," Temi di discussione (Economic working papers) 1023, Bank of Italy, Economic Research and International Relations Area.
    6. Hans Dewachter & Leonardo Iania & Jean-Charles Wijnandts, 2016. "The response of euro area sovereign spreads to the ECB unconventional monetary policies," Working Paper Research 309, National Bank of Belgium.
    7. Etienne Vaccaro-Grange, 2019. "Quantitative Easing and the Term Premium as a Monetary Policy Instrument," AMSE Working Papers 1932, Aix-Marseille School of Economics, France.
    8. Andrea Carriero & Sarah Mouabbi & Elisabetta Vangelista, 2018. "UK term structure decompositions at the zero lower bound," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(5), pages 643-661, August.
    9. Eric McCoy, 2019. "A Calibration of the Term Premia to the Euro Area," European Economy - Discussion Papers 2015 - 110, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
    10. Patrick Augustin & Mikhail Chernov & Dongho Song, 2018. "Sovereign Credit Risk and Exchange Rates: Evidence from CDS Quanto Spreads," NBER Working Papers 24506, National Bureau of Economic Research, Inc.
    11. Monfort, Alain & Pegoraro, Fulvio & Renne, Jean-Paul & Roussellet, Guillaume, 2017. "Staying at zero with affine processes: An application to term structure modelling," Journal of Econometrics, Elsevier, vol. 201(2), pages 348-366.
    12. Engle, Robert & Roussellet, Guillaume & Siriwardane, Emil, 2017. "Scenario generation for long run interest rate risk assessment," Journal of Econometrics, Elsevier, vol. 201(2), pages 333-347.
    13. Gouriéroux Christian & Monfort Alain & Mouabbi Sarah & Renne Jean-Paul, 2020. "Disastrous Defaults," Working papers 778, Banque de France.
    14. Bruna, Karel & Tran, Quang Van, 2020. "The central banks’ ability to control variability of money market interest rates: The case of inflation targeting countries," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 384-402.
    15. Andreasen, Martin M & Meldrum, Andrew, 2015. "Dynamic term structure models: the best way to enforce the zero lower bound in the United States," Bank of England working papers 550, Bank of England.
    16. S. Mouabbi, 2014. "An arbitrage-free Nelson-Siegel term structure model with stochastic volatility for the determination of currency risk premia," Working papers 527, Banque de France.
    17. Januj Amar Juneja, 2021. "How do invariant transformations affect the calibration and optimization of the Kalman filtering algorithm used in the estimation of continuous-time affine term structure models?," Computational Management Science, Springer, vol. 18(1), pages 73-97, January.
    18. Marcello Pericoli & Marco Taboga, 2018. "Nearly exact Bayesian estimation of non-linear no-arbitrage term structure models," Temi di discussione (Economic working papers) 1189, Bank of Italy, Economic Research and International Relations Area.
    19. Martin M. Andreasen & Andrew C. Meldrum, 2018. "A Shadow Rate or a Quadratic Policy Rule? The Best Way to Enforce the Zero Lower Bound in the United States," Finance and Economics Discussion Series 2018-056, Board of Governors of the Federal Reserve System (U.S.).
    20. Martin M. Andreasen & Andrew Meldrum, 2014. "Dynamic term structure models: The best way to enforce the zero lower bound," CREATES Research Papers 2014-47, Department of Economics and Business Economics, Aarhus University.
    21. Lemke, Wolfgang & Vladu, Andreea, 2015. "A Shadow-Rate Term Structure Model for the Euro Area," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113159, Verein für Socialpolitik / German Economic Association.
    22. Benjamin H Cohen & Peter Hördahl & Dora Xia, 2018. "Term premia: models and some stylised facts," BIS Quarterly Review, Bank for International Settlements, March.
    23. Bruno Feunou & Cédric Okou, 2018. "Risk‐neutral moment‐based estimation of affine option pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 1007-1025, November.

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    More about this item

    Keywords

    Zero lower bound; Affine process; Term structure model; Lift-off probabilities;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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