10. Consistency with VaR methodology

The Stressed VaR methodology should be based on the current VaR methodology, with specific techniques required, where applicable, in order to adjust the current VaR model into one that delivers a Stressed VaR measure. Any risk factor occurring in the VaR model should therefore be reflected in the Stressed VaR model.

With respect to standards used in both measures, and further to the ones prescribed by the Directive (e.g. the 99% confidence level), institutions may consider the use of ‘square root of time’ scaling to calculate a 10-day Stressed VaR measure. Nevertheless, given some known limitations of the scaling factor, an analysis to demonstrate that the assumptions underlying the use of the ‘square root of time’ rule are appropriate, should form part of the internal model validation process.

While the Stressed VaR model should share some of the current VaR standards, others may diverge due to explicit Directive requirements or to methodological incompatibilities related to the Stressed VaR concept. In particular, this is the case in the following areas:

• (i) Length of the stressed Period

Given the length of the stressed period must be 12 months, any action to reduce or increase the stated stressed period based on the need for consistency between VaR and Stressed VaR should not be permitted.

• (ii) Back-testing requirement

The multiplication factor m s used for capital requirements should be at least 3 and be increased by an addend between 0 and 1 depending on the VaR backtesting results. Nevertheless, backtesting is not a requirement in itself for determining the Stressed VaR measure.

• (iii) Periodicity of the Stressed VaR calculation

As the CRD provides that the calculation of the Stressed VaR should be at least weekly, institutions may choose to compute the measure more frequently, for instance, daily, to coincide with the VaR periodicity.

If, for example, institutions decide on a weekly Stressed VaR computation, and assuming a one-day Stressed VaR scaled up to 10 days, for the daily calculation of capital requirements based on internal models the following would apply:

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• a) The same Stressed VaR number would be used for 5 subsequent business days following the running of the Stressed VaR model;
• b) With respect to the calculation of the average Stressed VaR numbers during the preceding sixty business days, institutions should use the previous 12 Stressed VaR numbers to compute that average;
• c) An institution should be able to prove that, on the day of the week chosen for Stressed VaR calculation, its portfolio is representative of the portfolio held during the week and that the chosen portfolio does not lead to a systematical underestimation of the Stressed VaR numbers when computed weekly. For example, proof that the VaR is not systematically lower on the day of the week chosen for Stressed VaR calculation could be considered sufficient.

Stressed VaR standards may diverge from VaR standards in other circumstances where there could be methodological incompatibilities between the current VaR and the Stressed VaR model. One example includes changes in the current VaR methodology that cannot be translated into the Stressed VaR measure and the use of local valuation (sensitivity analysis/proxies) as opposed to full revaluation, which is the preferred approach for Stressed VaR.

As a general rule, changes in an institution’s VaR model or VaR methodology should be reflected in changes to the model/methodology used to calculate the Stressed VaR charge.

Under exceptional circumstances, if an institution can demonstrate that it cannot incorporate enhancements to the current VaR methodology in the Stressed VaR, such situations should be documented and the institution should be able to demonstrate that the impact (for example, in terms of VaR or capital requirements) resulting from the current VaR developments which are not implemented in the Stressed VaR measure is limited.

Where sensitivities rather than full revaluation are used within a VaR model, the institution concerned should demonstrate that this approach is still appropriate for Stressed VaR where larger shocks are applied. A sensitivity-based approach for Stressed VaR may require that higher order derivatives/convexity are factored in.

Any revaluation ladders or spot/volatility matrices employed should be reviewed and extended to include the wider shocks in risk factors that occur in stressful scenarios. It is preferable that full revaluation be used for Stressed VaR with shocks applied simultaneously to all risk factors.

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In terms of calibration to market data, the process of ‘de-meaning’ is not considered necessary for Stressed VaR. If there is a significant drift in market data, the use of antithetic data is preferable to ‘de-meaning’.

The table below summarises the main issues described above concerning the level of consistency between the methodological aspects of the current VaR and Stressed VaR measure.

Is consistency between VaR and Stressed VaR