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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
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    File URL: https://rem.rc.iseg.ulisboa.pt/wps/pdf/REM_WP_093_2019.pdf
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    References listed on IDEAS

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    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.
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