Business and Management

Quantile uncertainty and Value-at-Risk model risk

The finance industry’s reliance on Value-at-Risk (VaR) has been supported by decades of academic research. Especially during the last 10 years, there has been an explosion of articles published on this subject. The stark failure of many banks to set aside sufficient capital reserves during the banking crisis of 2008 sparked an intense debate on using VaR models for the purpose of computing the market risk capital requirements of banks.

Business Finance

Critics of VaR have warned about its application in risk assessment; the uncertainty surrounding these estimates has long been recognised. Nevertheless VaR remains the global standard for assessing risk in all types of financial firms.

The study

Professor Carol Alexander & J.M. Sarabia’s paper develops a methodology for quantifying model risk in quantile risk estimates and provides a novel and elegant framework whereby quantile estimates are adjusted for model risk, relative to a benchmark which represents the state of knowledge of the authority that is responsible for model risk. A simulation experiment in which the degree of model risk is controlled illustrates how to quantify Value-at-Risk model risk and compute the required regulatory capital add-on for banks.


An empirical example based on real data shows how the methodology can be put into practice, using only two time series (daily Value-at-Risk and daily profit and loss) from a large bank. The methodology has the potential to be applied to nonfinancial risks, including environmental risk assessment and statistical process control too.

The framework was validated and illustrated by a numerical example that considers three common VaR models in a simulation experiment where the degree of model risk has been controlled. A further empirical example describes how the model-risk adjustment could be implemented in practice given only two time series.


The paper develops a statistical methodology that provides a practical solution to the problem of quantifying the regulatory capital that should be set aside to cover the risk of producing inaccurate VaR estimates.

There is potential for extending the methodology to the quantile-based metrics that are commonly used to assess nonfinancial risks in hydrology, climate change, statistical process control and reliability analysis.

Access the paper

Alexander, Carol and Sarabia, José María (2012) Quantile uncertainty and value-at-risk model riskRisk Analysis: An International Journal, 32 (8). pp. 1293-1308. ISSN 1539-6924