An Heuristic Improvement of a Filtered Bootstrap Approach

Abstract

The purpose of this paper is to introduce an evolution of estimation of ex-ante VaR of the Monte Carlo Filtered Bootstrap. We define the "modus operandi" borrowing from Bayesian statistic the idea of prior, likelihood and posterior distribution to have a mixture distribution of future returns. We perform three tests, Unconditional Coverage, Independence and Conditional Coverage, according to Christoffersen (1998). We present results on both VaR1% and VaR5% on a one day horizon for the following indices: Standard&Poors 500, Topix, Dax, MSCI United Kingdom, MSCI France, Italy Comit Globale, MSCI Canada, MSCI Emerging Markets, RJ/CRB. We also test the model on a ten equities portfolios and over four commodity sector indices. Our results show that the improved Filtered Bootstrap approach satisfies Conditional Coverage for all tested indices and porfolios while the standard Filtered Bootstrap has more rejection cases. We also test the models in a regulatory framework (rolling window of 250 daily observations) and discuss the advantages of each method in the risk management process.