Displaced Historical Simulation is a Solution for Negative-Valued Financial Risk Values: Application to VaR in Times of Negative Government Bond Yields
Christian P. Fries
LMU Munich, Department of Mathematics; DZ Bank AG
University of St. Gallen
VU University Amsterdam
March 11, 2016
In this paper we introduce the displaced historical simulation model. The model makes possible historical simulations based on potentially negative risk variable, such as interest rates or spreads. This is an issue of recent and major interest to the financial sector, both from a regulatory and financial institutions perspective, especially in light of observed negative values for major bond yield and interest rate spread time series . Using historical simulation, the most widely used way of producing a distribution of possible future values of a risk variable is build around the concept of relative shifts (e.g. log-returns) applied to historical data. The relative shifts are "displaced" in an elegant way such that negative values can be handled. Our empirical results show that compared to other models in the literature, models equipped with our proposed displacement feature handle situations of close-to-zero or negative risk variables particularly well.
Number of Pages in PDF File: 40
Keywords: Historical simulation, generalizations, negative risk factors, Value at Risk
JEL Classification: C43, G17, G20, G30
Date posted: January 1, 2013 ; Last revised: March 12, 2016
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