IDEAS home Printed from https://ideas.repec.org/p/ise/remwps/wp0932019.html
   My bibliography  Save this paper

Pulled-to-Par Returns for Zero Coupon Bonds Historical Simulation Value at Risk

Author

Listed:
  • J. Beleza Sousa
  • Manuel L. Esquível
  • Raquel M. Gaspar

Abstract

Due to bond prices pull-to-par, zero coupon bonds historical returnsare not stationary, as they tend to zero as time to maturity approaches. Given that the historical simulation method for computing Value at Risk(VaR) requires a stationary sequence of historical returns, zero couponbonds historical returns can not be used to compute VaR by historical simulation. Their use would systematically overestimate VaR, resultingin invalid VaR sequences. In this paper we propose an adjustment of zero coupon bonds historical returns. We call the adjusted returns “pulled-to-par” returns. We prove that when the zero coupon bonds continuously compounded yields to maturity are stationary the adjusted pulled-to-parreturns allow VaR computation by historical simulation. We first illustrate the VaR computation in a simulation scenario,then we apply it to realdata on euro zone STRIPS.

Suggested Citation

  • J. Beleza Sousa & Manuel L. Esquível & Raquel M. Gaspar, 2019. "Pulled-to-Par Returns for Zero Coupon Bonds Historical Simulation Value at Risk," Working Papers REM 2019/93, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    • Handle: RePEc:ise:remwps:wp0932019
    as

    Download full text from publisher

    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_093_2019.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    2. Ant Afonso & Christophe Rault, 2015. "Short- and long-run behaviour of long-term sovereign bond yields," Applied Economics, Taylor & Francis Journals, vol. 47(37), pages 3971-3993, August.
    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. Olga Em & Georgi Georgiev & Sergey Radukanov & Mariana Petrova, 2022. "Assessing the Market Risk on the Government Debt of Kazakhstan and Bulgaria in Conditions of Turbulence," Risks, MDPI, vol. 10(5), pages 1-18, April.

    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. Hendry, David F. & Clements, Michael P., 2003. "Economic forecasting: some lessons from recent research," Economic Modelling, Elsevier, vol. 20(2), pages 301-329, March.
    2. Takahashi, Makoto & Watanabe, Toshiaki & Omori, Yasuhiro, 2016. "Volatility and quantile forecasts by realized stochastic volatility models with generalized hyperbolic distribution," International Journal of Forecasting, Elsevier, vol. 32(2), pages 437-457.
    3. Chen, Cathy W.S. & Gerlach, Richard & Hwang, Bruce B.K. & McAleer, Michael, 2012. "Forecasting Value-at-Risk using nonlinear regression quantiles and the intra-day range," International Journal of Forecasting, Elsevier, vol. 28(3), pages 557-574.
    4. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
    5. Rouba Ibrahim & Pierre L'Ecuyer, 2013. "Forecasting Call Center Arrivals: Fixed-Effects, Mixed-Effects, and Bivariate Models," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 72-85, May.
    6. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Realtime nowcasting with a Bayesian mixed frequency model with stochastic volatility," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(4), pages 837-862, October.
    7. M. Hashem Pesaran & Paolo Zaffaroni, 2004. "Model Averaging and Value-at-Risk Based Evaluation of Large Multi Asset Volatility Models for Risk Management," CESifo Working Paper Series 1358, CESifo.
    8. Dimitrakopoulos, Dimitris N. & Kavussanos, Manolis G. & Spyrou, Spyros I., 2010. "Value at risk models for volatile emerging markets equity portfolios," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 515-526, November.
    9. Qifa Xu & Lu Chen & Cuixia Jiang & Yezheng Liu, 2022. "Forecasting expected shortfall and value at risk with a joint elicitable mixed data sampling model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 407-421, April.
    10. Christophe Boucher & Benjamin Hamidi & Patrick Kouontchou & Bertrand Maillet, 2012. "Une évaluation économique du risque de modèle pour les investisseurs de long terme," Revue économique, Presses de Sciences-Po, vol. 63(3), pages 591-600.
    11. Szubzda Filip & Chlebus Marcin, 2019. "Comparison of Block Maxima and Peaks Over Threshold Value-at-Risk models for market risk in various economic conditions," Central European Economic Journal, Sciendo, vol. 6(53), pages 70-85, January.
    12. Ngozi G. Emenogu & Monday Osagie Adenomon & Nwaze Obini Nweze, 2020. "On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-25, December.
    13. Dinghai Xu & Tony S. Wirjanto, 2008. "An Empirical Characteristic Function Approach to VaR under a Mixture of Normal Distribution with Time-Varying Volatility," Working Papers 08008, University of Waterloo, Department of Economics.
    14. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    15. Mehmet Balcilar & Rangan Gupta & Stephen M. Miller, 2015. "The out-of-sample forecasting performance of nonlinear models of regional housing prices in the US," Applied Economics, Taylor & Francis Journals, vol. 47(22), pages 2259-2277, May.
    16. David E. Allen & Michael McAleer & Marcel Scharth, 2009. "Realized Volatility Risk," CIRJE F-Series CIRJE-F-693, CIRJE, Faculty of Economics, University of Tokyo.
    17. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    18. H. Kaibuchi & Y. Kawasaki & G. Stupfler, 2022. "GARCH-UGH: a bias-reduced approach for dynamic extreme Value-at-Risk estimation in financial time series," Quantitative Finance, Taylor & Francis Journals, vol. 22(7), pages 1277-1294, July.
    19. Massimiliano Marzo & Paolo Zagaglia, 2010. "Volatility forecasting for crude oil futures," Applied Economics Letters, Taylor & Francis Journals, vol. 17(16), pages 1587-1599.
    20. David E. Allen & Michael McAleer & Marcel Scharth, 2014. "Asymmetric Realized Volatility Risk," JRFM, MDPI, vol. 7(2), pages 1-30, June.

    More about this item

    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:ise:remwps:wp0932019. 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: Sandra Araújo (email available below). General contact details of provider: https://rem.rc.iseg.ulisboa.pt/ .

    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.