Pulled-to-par returns for zero coupon bonds : historical simulation value at risk - Sousa, J. Beleza (2019)
Due to bond prices pull-to-par, zero coupon bonds historical returns are 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 coupon bonds historical returns can not be used to compute VaR by historical simulation. Their use would systematically overestimate VaR, resulting in 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-par returns allow VaR computation by historical simulation. We first illustrate the VaR computation in a simulation scenario, then we apply it to real data on euro zone STRIPS.