Filtered Historical Simulation Value-at-Risk Models and Their Competitors

33 Pages Posted: 8 Mar 2015

See all articles by Pedro Gurrola-Perez

Pedro Gurrola-Perez

World Federation of Exchanges

David Murphy

London School of Economics - Law Department; Bank of England

Date Written: March 6, 2015


Financial institutions have for many years sought measures which cogently summarise the diverse market risks in portfolios of financial instruments. This quest led institutions to develop Value-at-Risk (VaR) models for their trading portfolios in the 1990s. Subsequently, so-called filtered historical simulation VaR models have become popular tools due to their ability to incorporate information on recent market returns and thus produce risk estimates conditional on them. These estimates are often superior to the unconditional ones produced by the first generation of VaR models. This paper explores the properties of various filtered historical simulation models. We explain how these models are constructed and illustrate their performance, examining in particular how filtering transforms various properties of return distribution. The procyclicality of filtered historical simulation models is also discussed and compared to that of unfiltered VaR. A key consideration in the design of risk management models is whether the model’s purpose is simply to estimate some percentile of the return distribution, or whether its aims are broader. We discuss this question and relate it to the design of the model testing framework. Finally, we discuss some recent developments in the filtered historical simulation paradigm and draw some conclusions about the use of models in this tradition for the estimation of initial margin requirements.

Keywords: Value-at-Risk, filtered historical simulation, conditional volatility, volatility scaling, risk model backtesting

JEL Classification: C58, G18, G32

Suggested Citation

Gurrola Perez, Pedro and Murphy, David, Filtered Historical Simulation Value-at-Risk Models and Their Competitors (March 6, 2015). Bank of England Working Paper No. 525, Available at SSRN: or

Pedro Gurrola Perez

World Federation of Exchanges ( email )

125 Old Broad Street
London, EC2N 1AR
United Kingdom
EC2N 1AR (Fax)


David Murphy (Contact Author)

London School of Economics - Law Department

Houghton Street
London WC2A 2AE, WC2A 2AE
United Kingdom

Bank of England ( email )

Threadneedle Street
London, EC2R 8AH
United Kingdom

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