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

J. Beleza Sousa, Manuel L. Esquível and Raquel Gaspar

No 2019/93, Working Papers REM from ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa

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.

Date: 2019-09
New Economics Papers: this item is included in nep-rmg
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