IDEAS home Printed from https://ideas.repec.org/p/bfr/banfra/558.html
   My bibliography  Save this paper

Staying at Zero with Affine Processes: An Application to Term Structure Modelling

Author

Listed:
  • A. Monfort
  • F. Pegoraro
  • J.-P. Renne
  • G. Roussellet

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 volatilities.

Suggested Citation

  • A. Monfort & F. Pegoraro & J.-P. Renne & G. Roussellet, 2015. "Staying at Zero with Affine Processes: An Application to Term Structure Modelling," Working papers 558, Banque de France.
    • Handle: RePEc:bfr:banfra:558
    as

    Download full text from publisher

    File URL: https://publications.banque-france.fr/sites/default/files/medias/documents/working-paper_558_2015.pdf
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jardet, Caroline & Monfort, Alain & Pegoraro, Fulvio, 2013. "No-arbitrage Near-Cointegrated VAR(p) term structure models, term premia and GDP growth," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 389-402.
    2. Christian Gourieroux & Alain Monfort & Fulvio Pegoraro & Jean-Paul Renne, 2014. "Regime Switching and Bond Pricing," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(2), pages 237-277.
    3. Lemke, Wolfgang & Vladu, Andreea L., 2016. "Below the zero lower bound: A shadow-rate term structure model for the euro area," Discussion Papers 32/2016, Deutsche Bundesbank.
    4. Leippold, Markus & Wu, Liuren, 2002. "Asset Pricing under the Quadratic Class," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(2), pages 271-295, June.
    5. 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.
    6. Pearson, Neil D & Sun, Tong-Sheng, 1994. " Exploiting the Conditional Density in Estimating the Term Structure: An Application to the Cox, Ingersoll, and Ross Model," Journal of Finance, American Finance Association, vol. 49(4), pages 1279-1304, September.
    7. Jens H. E. Christensen & Glenn D. Rudebusch, 2016. "Modeling Yields at the Zero Lower Bound: Are Shadow Rates the Solution?," Advances in Econometrics,in: Dynamic Factor Models, volume 35, pages 75-125 Emerald Publishing Ltd.
    8. Kim, Don H. & Orphanides, Athanasios, 2012. "Term Structure Estimation with Survey Data on Interest Rate Forecasts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 47(01), pages 241-272, April.
    9. Scott Joslin & Kenneth J. Singleton & Haoxiang Zhu, 2011. "A New Perspective on Gaussian Dynamic Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 24(3), pages 926-970.
    10. Black, Fischer, 1995. " Interest Rates as Options," Journal of Finance, American Finance Association, vol. 50(5), pages 1371-1376, December.
    11. Anna Cieslak & Pavol Povala, 2016. "Information in the Term Structure of Yield Curve Volatility," Journal of Finance, American Finance Association, vol. 71(3), pages 1393-1436, June.
    12. Jing Cynthia Wu & Fan Dora Xia, 2016. "Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(2-3), pages 253-291, March.
    13. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2013. "Pricing the term structure with linear regressions," Journal of Financial Economics, Elsevier, vol. 110(1), pages 110-138.
    14. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    15. Refet S. Gürkaynak & Jonathan H. Wright, 2012. "Macroeconomics and the Term Structure," Journal of Economic Literature, American Economic Association, vol. 50(2), pages 331-367, June.
    16. Creal, Drew D. & Wu, Jing Cynthia, 2015. "Estimation of affine term structure models with spanned or unspanned stochastic volatility," Journal of Econometrics, Elsevier, vol. 185(1), pages 60-81.
    17. Ruslan Bikbov & Mikhail Chernov, 2011. "Yield Curve and Volatility: Lessons from Eurodollar Futures and Options," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(1), pages 66-105, Winter.
    18. 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..
    19. Hibiki Ichiue & Yoichi Ueno, 2013. "Estimating Term Premia at the Zero Bound: An Analysis of Japanese, US, and UK Yields," Bank of Japan Working Paper Series 13-E-8, Bank of Japan.
    20. Almeida, Caio & Graveline, Jeremy J. & Joslin, Scott, 2011. "Do interest rate options contain information about excess returns?," Journal of Econometrics, Elsevier, vol. 164(1), pages 35-44, September.
    21. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. "Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-135, September.
    22. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    23. Jacobs, Kris & Karoui, Lotfi, 2009. "Conditional volatility in affine term-structure models: Evidence from Treasury and swap markets," Journal of Financial Economics, Elsevier, vol. 91(3), pages 288-318, March.
    24. Don H. Kim, 2008. "Zero bound, option-implied PDFs, and term structure models," Finance and Economics Discussion Series 2008-31, Board of Governors of the Federal Reserve System (US).
    25. repec:eee:econom:v:201:y:2017:i:2:p:348-366 is not listed on IDEAS
    26. Krippner, Leo, 2013. "Measuring the stance of monetary policy in zero lower bound environments," Economics Letters, Elsevier, vol. 118(1), pages 135-138.
    27. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    28. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
    29. Serge Darolles & Christian Gourieroux & Joann Jasiak, 2006. "Structural Laplace Transform and Compound Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 477-503, July.
    30. Jens H. E. Christensen & Glenn D. Rudebusch, 2015. "Estimating Shadow-Rate Term Structure Models with Near-Zero Yields," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(2), pages 226-259.
    31. Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, August.
    32. Kozicki, Sharon & Tinsley, P. A., 2001. "Term structure views of monetary policy under alternative models of agent expectations," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 149-184, January.
    33. Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2015. "A Quadratic Kalman Filter," Journal of Econometrics, Elsevier, vol. 187(1), pages 43-56.
    34. Yoichi Ueno & Naohiko Baba & Yuji Sakurai, 2006. "The Use of the Black Model of Interest Rates as Options for Monitoring the JGB Market Expectations," Bank of Japan Working Paper Series 06-E-15, Bank of Japan.
    35. Renne Jean-Paul, 2017. "A model of the euro-area yield curve with discrete policy rates," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 99-116, February.
    36. Anders B. Trolle & Eduardo S. Schwartz, 2009. "A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 2007-2057, May.
    37. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
    38. 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.
    39. Alain Monfort & Fulvio Pegoraro & Jean-Paul Renne & Guillaume Roussellet, 2017. "Staying at zero with affine processes : an application to term structure modelling," Rue de la Banque, Banque de France, issue 52, november.
    40. Kim, Don H. & Singleton, Kenneth J., 2012. "Term structure models and the zero bound: An empirical investigation of Japanese yields," Journal of Econometrics, Elsevier, vol. 170(1), pages 32-49.
    41. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    42. Leo Krippner, 2011. "Modifying Gaussian term structure models when interest rates are near the zero lower bound," CAMA Working Papers 2011-36, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    43. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    44. Christensen, Jens H.E. & Lopez, Jose A. & Rudebusch, Glenn D., 2014. "Can Spanned Term Structure Factors Drive Stochastic Yield Volatility?," Working Paper Series 2014-3, Federal Reserve Bank of San Francisco.
    45. Duffee, Gregory R., 2013. "Bond Pricing and the Macroeconomy," Handbook of the Economics of Finance, Elsevier.
    46. Kozicki, Sharon & Tinsley, P. A., 2001. "Shifting endpoints in the term structure of interest rates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 613-652, June.
    47. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    48. Anh Le & Kenneth J. Singleton & Qiang Dai, 2010. "Discrete-Time Affine-super-ℚ Term Structure Models with Generalized Market Prices of Risk," Review of Financial Studies, Society for Financial Studies, vol. 23(5), pages 2184-2227.
    49. Marcel A. Priebsch, 2013. "Computing arbitrage-free yields in multi-factor Gaussian shadow-rate term structure models," Finance and Economics Discussion Series 2013-63, Board of Governors of the Federal Reserve System (US).
    50. Haitao Li & Feng Zhao, 2006. "Unspanned Stochastic Volatility: Evidence from Hedging Interest Rate Derivatives," Journal of Finance, American Finance Association, vol. 61(1), pages 341-378, February.
    51. Tobias Adrian & Hao Wu, 2009. "The term structure of inflation expectations," Staff Reports 362, Federal Reserve Bank of New York.
    52. Michael D. Bauer & Glenn D. Rudebusch, 2016. "Monetary Policy Expectations at the Zero Lower Bound," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(7), pages 1439-1465, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Richhild Moessner, 2018. "Effects of asset purchases and financial stability measures on term premia in the euro area," Applied Economics, Taylor & Francis Journals, vol. 50(43), pages 4617-4631, September.
    2. repec:wly:jmoncb:v:51:y:2019:i:5:p:1053-1096 is not listed on IDEAS
    3. King, Thomas B., 2016. "Expectation and Duration at the Effective Lower Bound," Working Paper Series WP-2016-21, Federal Reserve Bank of Chicago.
    4. 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.
    5. 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.
    6. 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.
    7. Olesya Grishchenko & Sarah Mouabbi & Jean‐Paul Renne, 2019. "Measuring Inflation Anchoring and Uncertainty: A U.S. and Euro Area Comparison," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(5), pages 1053-1096, August.
    8. repec:wly:japmet:v:33:y:2018:i:6:p:763-779 is not listed on IDEAS
    9. 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.
    10. 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 (US).
    11. 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.
    12. Lemke, Wolfgang & Vladu, Andreea, 2015. "A Shadow-Rate Term Structure Model for the Euro Area," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113159, Verein für Socialpolitik / German Economic Association.
    13. repec:bis:bisqtr:1809h is not listed on IDEAS
    14. repec:wly:japmet:v:33:y:2018:i:7:p:1007-1025 is not listed on IDEAS
    15. 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.
    16. 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.
    17. repec:bfr:rueban:2017:52 is not listed on IDEAS
    18. repec:eee:jimfin:v:88:y:2018:i:c:p:296-313 is not listed on IDEAS
    19. repec:eee:econom:v:201:y:2017:i:2:p:333-347 is not listed on IDEAS
    20. Alain Monfort & Fulvio Pegoraro & Jean-Paul Renne & Guillaume Roussellet, 2017. "Staying at zero with affine processes : an application to term structure modelling," Rue de la Banque, Banque de France, issue 52, november.

    More about this item

    Keywords

    Zero Lower Bound; Affine Process; Term-Structure Model; Lift-Off probabilities;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bfr:banfra:558. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Michael brassart). General contact details of provider: http://edirc.repec.org/data/bdfgvfr.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.