An optimal framework would be a combination of both approaches depending on the data quality of risk factors:
- When a risk factor has sufficient data quality, direct determination of the extreme scenario of a future shock for a NMRF over the selected stressed period (Option A) is preferable to any rescaling of a current window shock that could be obtained looking at MRF (B).
- However, when considering the stressed window calibration process associated to the two options, it is also evident that the stressed period calibration associated to option A is computationally too intensive and not pursuable in its current form.
- In case the stressed window calibration approach could be disentangled from the determination of the stressed scenario, option A would be preferable to option B (only for those risk factors with sufficient data quality across the stressed period).
In case alternative proposals to the calibration of the stressed window were not considered (e.g. Q 12) then option B would be the only implementable solution.
Option A is only applicable to NMRF with sufficient data quality over a stressed period (which might even mean 12 observations if the sigma approach was allowed) while Option B is more suitable for NMRF without enough observations over the stressed period.
This shows that – over a given stressed window – the two approaches for the determination of the stressed shocks could be contextually used for risk-factors with different data quality.
We do not believe that Direct Method could be used in practice due to the computational effort it requires, especially in the context of the stressed window calibration.
I.e. since the direct method is only considered in association to option A for the calibration of the stressed window (and the consequent definition of the stressed shock) it will be overly burdensome to turn into a productive implementation.
Admittedly, even leaving aside the stressed calibration window, the calculation of an ES in Full Revaluation for each NMRF will end up requiring many more revaluations than the IMCC calculation (already much more demanding than Basel 2.5 metrics).
The contoured shift option in that more closely represents the characteristics of the individual risk factors embedded in a regulatory bucket.
The proposed approach does not pose concerns.
The sigma method, primarily to stick to an uncontroversial metric that does not open for additional degrees of freedom in its determination (e.g. how to split return).
The constant depends clearly on the empirical distribution. Three seems on the conservative side.
Uncertainty compensation factor should be 1 if there is full data used (ie 250 data points in the historical method). The uncertainty formula should be adjusted to achieve that.
Due to formulas, which are part of the response to this question and cannot be properly displayed in this form, we would like to refer to the response to question 9 of the attached document.
Not to additionally complicate the methodology for such corner cases, we would favor a simpler option, a mapping to one of the SBM RW.
The algorithm for the identification of the stress period under option A (maximization of the losses stemming from the direct method for each Broad Risk Category (BRC) is simply not manageable and drives the choice to Option B.
Indeed the number of instrument revaluations required to calibrate the stressed window for each BRC can quickly become unmanageable. We explain the point through a comparison with the UES calibration approach used for the ES part of IMA.
• From 2007 to today there are about 3500 10-day returns
• The calibration of UES for a Bond in (e.g.) CZK for an EU Bank requires 3500 revaluations of the Bond which are then aggregated in 250-sets to identify the one with the highest ES.
• The calibration of SES for the same bond depends on:
1. The number of non Modellable buckets for each RF (e.g. 3 buckets for CS and 4 buckets for IR; FX is instead Modellable x7
2. Use of Direct Method ( x250) vs the used of the Step Wise Method (x6 grid-points)
• This could hence result in either 3500 revaluations for each NMRF aggregated in 250-sets to identify the set with the highest ES (Direct approach: 3500x7 revaluations of the bond ) or 6 revaluations within each of the stressed periods that can be identified between 2007-today; for historical return method, due to the overlap between periods it is conceivable that this results in 3250*5% windows, where 5% represents the tails over which ES is computed in each window. As a result the number of revaluations of the bond could be 3250*5%x6x7.
• For sigma method, there is not overlap as even a 1-day change of the period changes the Stdev of the returns and as a result the number of revaluations of the bond could be 3250x6x7.
• While the calibration through the step-wise method could look computationally lighter than the UES calibration, it nevertheless shows a linear dependence to the pairs InstrumentWithNMRF x NMRF that can quickly become larger than the overall number of Instruments in the portfolio. In this example the number of revaluations is milder than the UES calibration but it is due to the fact that we are considering a single instrument and 7 NMRF. For a real life portfolio with hundred thousands of instruments and thousands of NMRF the computational burden will clearly blow out.
In order to substantially reduce the computational needs to a manageable level, firms could be allowed to use a sensitivity approach to determine the stress window even though those risk factors may be modelled for capital (ES, SES) under a full revaluation approach.
Alternatively, a proposed approach would be to use a RF based approach as is used in Option B to identify the stressed period per BRC and to make the assumption that a worse stress period for the modelled risk factors is a suitable period to use for the SES for that broad risk class.
When for a NMRF the maximum loss is non-finite loss, banks should be allowed to provide an alternative expert based stress scenario using qualitative and quantitative information calibrated to be at least as conservative as a 97.5% stressed ES and not the 99.95% proposed by the draft RTS, which would result in another element of conservativism to the framework.
In the ES or VaR model shifts to curves or surfaces are applied in a scenario consistent way, ie all the points on that curve or surface are jointly shifted according to the historical realized dynamic. Therefore, pricing issues resulting from the application of large shifts to only one portion of the curve/surface are not really frequent so that at the moment the affected instrument is removed by that particular scenario.
On the contrary for SES calculation a stress shift is applied to only one part of a curve or surface so this is an important point to consider.
However in practice NMRF will be decomposed into a portion that is included in the ES model and a basis that is used in the SES. The fact that the SES basis shifts will be smaller than the outright RF shifts already embeds a natural mitigation. It is however conceivable that shifting only a portion of a curve/surface will still lead to pricing errors. Therefore it would be useful to introduce mechanisms and safety valves that could be applied and give resilience if this does arise.
The fundamental problem, that can occur when a small portion of a curve is shifted by a large amount and the other parts are left constant, is that the shift size amount is unrealistically large versus the parts that are not shifted and this breaks the consistency of the curve or surface that is applied in a stress (and what is applied, is economically meaningless).
When a non-pricing scenario is identified for certain product/pricer combination, the banks should be allowed to adjust the scenarios for the product/pricer combination in question. Such adjustment includes e.g. de-arbitration, imposing floor/cap, and etc. The adjusted scenario should be permitted as long as banks can provide sufficient documentation on the methodology and evidence of the case when this adjustment is applied should be tracked and made available to competent authorities.
The risk factors reflecting idiosyncratic credit spread risk and idiosyncratic equity risk are aggregated with zero correlation. NMRF basis will be created by decomposing NMRF into a component that is suitable to represent the RF in the ES model and a residual basis. This choice of decomposition will be driven by getting as a good representation of the RF in the ES model. The residual basis should not be correlated. The condition under (b) can be too specific, so propose a modification.
Change clause (b) as follows: “the value taken by the risk factor should not be systematically correlated with other credit (equity) idiosyncratic factors”
Change clause (c) as follows: “the institution performs and documents the statistical tests that are used to verify point (b). This can include tests that prove values taken are not driven by systematic risk components.
Yes, to simplify the framework a bit.
The scaler in its current definition is prone to spikes in those cases where a BRC is dominated by MRFs with a very low standard deviation over the current period. The trimming could help in this context however the effectiveness depends on the relative presence of such types of risk factors among the MRFs of the BRC. In case the difference in volatility between current and stressed period is the result of a change in market regime (e.g. negative rates) such extreme re-scaling would not be necessarily appropriate, especially because it would then affect any other risk factor in that BRC.
A relevant example can be identified with EUR rates in particular over the short term pillars where the insurgence of negative rates has also caused a significant compression of the standard deviation over the current window. Current trimming at 1% can be effective in reducing such extreme cases only to the extent that these risk-factors represent 1% of the MRF for the affected BRC. For a portfolio dominated by EUR this might not be the case.
In order to reduce the effect it would be beneficial to allow a higher trimming for those BRC (i.e. IR) where this effect is visible to an amount that reflects the relative presence of these types of RF among the MRF of that BRC. The refinement of the trimming confidence level would have to be documented.
We would propose using for that BRC the scale used to scale the ESF,C in the IMCC portion of the IMA, i.e. ESR,S /ESR,C