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Quantile Uncertainty and Value‐at‐Risk Model Risk
Author(s) -
Alexander Carol,
Sarabia José María
Publication year - 2012
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/j.1539-6924.2012.01824.x
Subject(s) - quantile , value at risk , basel ii , risk management , economic capital , actuarial science , econometrics , operational risk , estimation , financial risk management , expected shortfall , market risk , model risk , coherent risk measure , economics , risk assessment , risk analysis (engineering) , capital requirement , profit (economics) , business , finance , management , microeconomics
This article develops a methodology for quantifying model risk in quantile risk estimates. The application of quantile estimates to risk assessment has become common practice in many disciplines, including hydrology, climate change, statistical process control, insurance and actuarial science, and the uncertainty surrounding these estimates has long been recognized. Our work is particularly important in finance, where quantile estimates (called Value‐at‐Risk) have been the cornerstone of banking risk management since the mid 1980s. A recent amendment to the Basel II Accord recommends additional market risk capital to cover all sources of “model risk” in the estimation of these quantiles. We provide 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. We conclude with a discussion of potential applications to nonfinancial risks.