IDEAS home Printed from https://ideas.repec.org/a/ris/apltrx/0462.html
   My bibliography  Save this article

Dynamic Nelson–Siegel model for market risk estimation of bonds: Practical implementation

Author

Listed:
  • Makushkin, Mikhail

    (HSE University, Moscow, Russian Federation;)

  • Lapshin, Victor

    (HSE University, Moscow, Russian Federation;)

Abstract

The article is devoted to Value-at-Risk estimation of bonds based on Dynamic Nelson–Siegel model (DNS). Instead of dealing with estimation of future interest rates and their volatiles, DNS model forecasts several unobservable shape parameters of the yield curve. We illustrate that for practical purposes one factor model is enough to correctly estimate bond VaR — this factor being long-term level of interest rates. We recommend to use AR(1)-GARCH(1,1) model to describe the evolution of interest rates level. Such dynamics specification provides accurate risk estimates while minimizing the number of consecutive VaR violations. We emphasize that the choice of optimization algorithm for estimation of yield curve parameters is crucial for accurate VaR forecasting since it might bring additional model noise into time series of yield curve parameters.

Suggested Citation

  • Makushkin, Mikhail & Lapshin, Victor, 2023. "Dynamic Nelson–Siegel model for market risk estimation of bonds: Practical implementation," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 69, pages 5-27.
    • Handle: RePEc:ris:apltrx:0462
    as

    Download full text from publisher

    File URL: http://pe.cemi.rssi.ru/pe_2023_69_005-027.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Yu, Wei-Choun & Zivot, Eric, 2011. "Forecasting the term structures of Treasury and corporate yields using dynamic Nelson-Siegel models," International Journal of Forecasting, Elsevier, vol. 27(2), pages 579-591, April.
    3. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    4. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Nagy, Krisztina, 2020. "Term structure estimation with missing data: Application for emerging markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 75(C), pages 347-360.
    7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    8. Ferreira, Miguel A., 2005. "Forecasting the comovements of spot interest rates," Journal of International Money and Finance, Elsevier, vol. 24(5), pages 766-792, September.
    9. Miguel A. Ferreira, 2005. "Evaluating Interest Rate Covariance Models Within a Value-at-Risk Framework," Journal of Financial Econometrics, Oxford University Press, vol. 3(1), pages 126-168.
    10. 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.
    11. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    12. 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.
    13. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    14. Ranik Raaen Wahlstrøm & Florentina Paraschiv & Michael Schürle, 2022. "A Comparative Analysis of Parsimonious Yield Curve Models with Focus on the Nelson-Siegel, Svensson and Bliss Versions," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 967-1004, March.
    15. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    16. 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..
    17. Diebold, Francis X. & Rudebusch, Glenn D. & Borag[caron]an Aruoba, S., 2006. "The macroeconomy and the yield curve: a dynamic latent factor approach," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 309-338.
    18. Vlaar, Peter J. G., 2000. "Value at risk models for Dutch bond portfolios," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1131-1154, July.
    19. Chen, Ren-Raw & Scott, Louis, 2003. "Multi-factor Cox-Ingersoll-Ross Models of the Term Structure: Estimates and Tests from a Kalman Filter Model," The Journal of Real Estate Finance and Economics, Springer, vol. 27(2), pages 143-172, September.
    20. Koopman, Siem Jan & Mallee, Max I. P. & Van der Wel, Michel, 2010. "Analyzing the Term Structure of Interest Rates Using the Dynamic Nelson–Siegel Model With Time-Varying Parameters," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 329-343.
    21. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    22. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    23. Joel Barber & Mark Copper, 2012. "Principal component analysis of yield curve movements," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 36(3), pages 750-765, July.
    24. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    25. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    26. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    27. Mikhail Makushkin & Victor Lapshin, 2021. "Yield Curve Estimation in Illiquid Bond Markets," HSE Economic Journal, National Research University Higher School of Economics, vol. 25(2), pages 177-195.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Caldeira, João F. & Laurini, Márcio P. & Portugal, Marcelo S., 2010. "Bayesian Inference Applied to Dynamic Nelson-Siegel Model with Stochastic Volatility," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(1), October.
    2. Wali ULLAH & Khadija Malik BARI, 2018. "The Term Structure of Government Bond Yields in an Emerging Market," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 5-28, September.
    3. Ranik Raaen Wahlstrøm & Florentina Paraschiv & Michael Schürle, 2022. "A Comparative Analysis of Parsimonious Yield Curve Models with Focus on the Nelson-Siegel, Svensson and Bliss Versions," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 967-1004, March.
    4. Rui Chen & Jiri Svec & Maurice Peat, 2016. "Forecasting the Government Bond Term Structure in Australia," Australian Economic Papers, Wiley Blackwell, vol. 55(2), pages 99-111, June.
    5. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Effects on the Riskless Yield Curve with Regime Switching Nelson†Siegel Models," Working Papers 639, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Hautsch, Nikolaus & Ou, Yangguoyi, 2012. "Analyzing interest rate risk: Stochastic volatility in the term structure of government bond yields," Journal of Banking & Finance, Elsevier, vol. 36(11), pages 2988-3007.
    7. Jiazi Chen & Zhiwu Hong & Linlin Niu, 2022. "Forecasting Interest Rates with Shifting Endpoints: The Role of the Demographic Age Structure," Working Papers 2022-06-25, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    8. João Caldeira & Guilherme Moura & André Santos, 2015. "Measuring Risk in Fixed Income Portfolios using Yield Curve Models," Computational Economics, Springer;Society for Computational Economics, vol. 46(1), pages 65-82, June.
    9. Guidolin, Massimo & Thornton, Daniel L., 2018. "Predictions of short-term rates and the expectations hypothesis," International Journal of Forecasting, Elsevier, vol. 34(4), pages 636-664.
    10. Molenaars, Tomas K. & Reinerink, Nick H. & Hemminga, Marcus A., 2013. "Forecasting the yield curve - Forecast performance of the dynamic Nelson-Siegel model from 1971 to 2008," MPRA Paper 61862, University Library of Munich, Germany.
    11. Siem Jan Koopman & Max I.P. Mallee & Michel van der Wel, 2007. "Analyzing the Term Structure of Interest Rates using the Dynamic Nelson-Siegel Model with Time-Varying Parameters," Tinbergen Institute Discussion Papers 07-095/4, Tinbergen Institute.
    12. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Switching Nelson-Siegel Models," BAFFI CAREFIN Working Papers 19106, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    13. Choong Tze Chua & Dean Foster & Krishna Ramaswamy & Robert Stine, 2008. "A Dynamic Model for the Forward Curve," The Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 265-310, January.
    14. Christensen, Bent Jesper & van der Wel, Michel, 2019. "An asset pricing approach to testing general term structure models," Journal of Financial Economics, Elsevier, vol. 134(1), pages 165-191.
    15. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.
    16. Kaya, Huseyin, 2013. "Forecasting the yield curve and the role of macroeconomic information in Turkey," Economic Modelling, Elsevier, vol. 33(C), pages 1-7.
    17. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    18. Jan Hanousek & Evžen KoÄ enda & Petr ZemÄ Ã­k, 2008. "Bond Market Emergence," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 7(2), pages 141-168, August.
    19. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    20. Nagy, Krisztina, 2020. "Term structure estimation with missing data: Application for emerging markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 75(C), pages 347-360.

    More about this item

    Keywords

    market risk; risk management; Value-at-Risk; bonds; interest rate; term structure; Nelson–Siegel model.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:ris:apltrx:0462. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Anatoly Peresetsky (email available below). General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.