Sovereign Risk: How Filtered Bootstrap and Historical Simulation Catch Government Problems

Abstract

The purpose of this paper is to apply the results of Brandolini D. – Colucci S. “Backtesting Value-at-Risk: A comparison between Filtered Bootstrap and Historical Simulation” in order to extend the VaR estimation also in a bond universe and particularly in order to estimate sovereign risk. We see a comparison between two risk models to evaluate, VaR, Historical Simulation and Monte Carlo Filtered Bootstrap. We perform three tests, Unconditional Coverage, Independence and Conditional Coverage as in Christoffersen, P., Pellettier D. (2004) paper. We present results on both VaR 1% both VaR 5% in one day horizon for the two models on seven sovereign bond proxed by the following indices: Merril Lynch German Federal Governments, 7-10y (G4D0 as BUND), Merril Lynch Portuguese Governments, 7-10y (G4U0 as PGB), Merril Lynch Irish Governments, 7-10y (G4R0 as IRISH), Merril Lynch Italian Governments, 7-10y (G4I0 as BTP), Merril Lynch Spanish Governments, 7-10y (G4E0 as BONOS), Merril Lynch Emerging Market Sovereigns, Greece (GDGR as GGB) and Merril Lynch US Treasury 7-10y (G4A0) all in Local Currency. Our results show that Filtered Bootstrap Approach satisfy all test for all indices, while Historical Simulation has many rejection cases. Finally we also test in a regulatory framework (rolling window of 250 observations) the two models and the advantages of using a conditional coverage methodology to validate risk models.

Keywords: VaR, Backtest, Filtered Bootstrap, Historical Simalation, Sovereign Risk

JEL Classification: C22, G22, G23, G24