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Displaced Relative Changes in Historical Simulation: Application to Risk Measures of Interest Rates with Phases of Negative Rates

Christian P. Fries

LMU Munich, Department of Mathematics; DZ Bank AG

Tobias Nigbur

University of St. Gallen

Norman Seeger

VU University Amsterdam

March 11, 2016

In this paper we introduce the displaced historical simulation model which is designed to handle negative and close-to-zero risk factors. 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. In historical simulation a common approach is to consider log returns (that is, relative changes), given that the risk factors remain positive. If a risk factor allows for negative values, log returns cannot be applied and one either ignores such scenarios or switches to considering absolute changes. The latter approach implies an abrupt model change. Our displaced historical simulation model strongly improves the historical simulation by "displacing" the shifts such that negative values can be handled, smoothly moving to the limit case of using absolute shifts instead of relative shifts of the original data. Our empirical results show that compared to other models presented 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: 39

Keywords: Historical simulation, generalizations, negative risk factors, Value at Risk

JEL Classification: C43, G17, G20, G30

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Date posted: January 1, 2013 ; Last revised: September 19, 2016

Suggested Citation

Fries, Christian P. and Nigbur, Tobias and Seeger, Norman, Displaced Relative Changes in Historical Simulation: Application to Risk Measures of Interest Rates with Phases of Negative Rates (March 11, 2016). Available at SSRN: http://ssrn.com/abstract=2194917 or http://dx.doi.org/10.2139/ssrn.2194917

Contact Information

Christian P. Fries (Contact Author)
LMU Munich, Department of Mathematics ( email )
Theresienstrasse 39
DZ Bank AG ( email )
60265 Frankfurt am Main
Tobias Nigbur
University of St. Gallen ( email )
Norman Seeger
VU University Amsterdam ( email )
De Boelelaan 1105
Amsterdam, 1081 HV
+31 20 598 1512 (Phone)
HOME PAGE: http://www.norman-seeger.com
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