Learning by Failing: A Simple VaR Buffer

Abstract

International audienceWe study in this article the problem of model risk in VaR computations and document a procedure for correcting the bias due to specification and estimation errors. This practical method consists of “learning from model mistakes”, since it dynamically relies on an adjustment of the VaR estimates – based on a back-testing framework – such as the frequency of past VaR exceptions always matches the expected probability. We finally show that integrating the model risk into the VaR computations implies a substantial minimum correction to the order of 10–40% of VaR levels

An Economic Evaluation of Model Risk in Long‐term Asset Allocations

“…In this paper, we first illustrate and estimate the model risk of risk models (see also Boucher and Maillet, ) and we evaluate its impact on long‐term asset allocations. First, we evaluate the simple effect of estimation and specification risks on VaR estimates.…”

“…The first column in each block related to a process represents the Mean Estimated VaR with specification and estimation errors, whilst the following cells indicate the mean‐minimum‐maximum of the adjustment term corresponding to the observed differences between the Imperfect Historical‐simulated Estimated VaR, empirically recovered in 250,000 draws of limited samples of 250, 300 or 350 daily returns (Panel A, B and C), and the asymptotic (true) VaR (computed with the 250,000 data points of the full original sample for each process). Per convention, a negative adjustment term in the table indicates that the Estimated VaR (negative return) should be more conservative (more negative); see Aït‐Sahalia et al () and Boucher and Maillet () for more details. Simulations by the authors.…”

Market Risk and Volatility Weighted Historical Simulation after Basel III

“…-Regulatory backtesting will be conducted at a more granular (desk) level and involves a set of indicators, daily VaR exceptions at both 97.5% and 99% levels, p-values, daily 97.5% one day 97.5% Expected Shortfall 13 . -The capital metrics involves computation based on shocks on risk factors over a base liquidity horizon of 10 days (FRTB §181 c).…”

“…In all cases, the derivation depends on the chosen estimation technique and perhaps more importantly on the length of the data sample. 13 Failure to comply with new backtesting requirements leads to ineligibility of trading desks to the Internal Models Approach (IMA) and a fall-back to the Standardised Approach (SA), associated with more stringent capital requirements. According to ISDA, based on the outcome of the June 2015 Basel Committee Quantitative Impact Study, the ratio of SA capital requirements to the risk measure derived from internal expected shortfall models would range from 2.1 to 4.6 depending on the risk factor class Industry FRTB QIS Analysis, https://www2.isda.org/attachment/Nzk0OA==/Industry%20FRTB%20QIS%20Analysis%20Executive%20Summa ry%20OCT%202015.pdf 14 Under the Basel Committee prescriptions, internal models should be at least as granular as the standard approach, thus the number of risk factors associated with IMA is floored by the number of risk factors involved in SA.…”