InternalModelApproach

All measures in this section disregard the actual capital treatment of individual positions and compute charges as if all positions were under IMA approach.

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CA

Formula $C_A=max\left \{ IMCC_{t-1} + SES_{t-1}; m_c \cdot IMCC_{avg}+SES_{avg} \right \}$

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ES (Basic Non-Modellable Idiosyncratic)

A technical measure used in the expected shortfall calculation for non-modellable idiosyncratic risk factors.

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ES (Basic Non-Modellable Idiosyncratic) Differential

A technical measure computed on the reference-shifted (Differential) idiosyncratic NMRF P&L vector. It feeds the Incremental variation of ES (ISES).

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ES (Basic Non-Modellable Non-Idiosyncratic)

A technical measure used in the expected shortfall calculation for non-modellable non-idiosyncratic risk factors.

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ES (Basic Non-Modellable Non-Idiosyncratic) Differential

A technical measure computed on the reference-shifted (Differential) non-idiosyncratic NMRF P&L vector. It feeds the Incremental variation of ES (SES).

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ES (Basic)

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ES (Basic).D2D

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ES (Capital Constrained)

The measure takes the results of ES (Capital) calculation for the individual Risk Classes (not ‘allin’) and then sums them up.

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ES (Capital Unconstrained)

Formula $IMCC(C)=ES_{R,S} \cdot \frac{ES_{F,C} }{ES_{R,C} }$ This measure represents expected shortfall across risk classes, liquidity-adjusted and scaled to stress period. Also referred to as “unconstrained”.

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ES (Capital)

Formula $ES = ES_{R,S} \cdot \frac{ES_{F,C}}{ES_{R,C}}$ The measure takes the result of the ES (Liquidity Adj.) measure filtered by the [Risk].[Data Sets] equal to ‘Reduced Set Stressed’. It then scales that result by a ratio. The ratio is the ES (Liquidity Adj.) for [Risk].[Data Sets] equal to ‘Full Set Current’ divided by the ES (Liquidity Adj.) for the ‘Reduced Set Current’. Note that the ratio of the ES (Liquidity Adj.) for the [Risk].[Data Sets] equal to ‘Full Set Current’ and ES (Liquidity Adj.) for the ‘Reduced Set Current’ can be displayed using ES (Current Ratio).

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ES (Current Ratio)

Formula $\max\left(\frac{ES_{F,C}}{ES_{R,C}},1\right)$

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ES (ISES)

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ES (ISES) Differential

Equal to $-1 \times$ ES (Basic Non-Modellable Idiosyncratic) Differential. It feeds the Incremental variation of ES (ISES).

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ES (Liquidity Adj.)

Formula $ES = \sqrt{\left(ES_T(P)\right)^2 + \sum_{j\geq 2}\left(ES_T(P,j)\sqrt{\frac{(LH_j - LH_{j-1})}{T}}\right)^2}$ This measure applies liquidity horizons adjustment to the ES (Basic) measure. This measure needs to be combined with [Risk].[Risk Classes] and [Risk].[Data Sets] to produce a business interpretable result.

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ES (Liquidity Horizon Adjusted Euler)

Formula $ES_{\text{Euler}} = \frac{ES_{\text{Liq Hor Adj Sq Euler}}}{ES_{\text{Liquidity Adj. Reference}}}$

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ES (Model Variation)

Formula $\frac{ES_{R,C}}{ES_{F,C}}$ To evaluate how much variation of the full ES model is explained by the reduced set of risk-factors (MAR 33.5 (2) (b)), the ES (Model Variation) avg measure should be evaluated for the allin risk-class. The ES (Model Variation) measure is the ratio of the ES (Liquidity Adj.) measures for the reduced and full sets of risk factors (over the current data set), that is $ES_{R,C} / ES_{F,C}$. As per MAR33.5 (2) (b), this ratio should average over 75% for the last 12 weeks.

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ES (SES)

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ES (SES) Differential

Equal to $-1 \times$ ES (Basic Non-Modellable Non-Idiosyncratic) Differential. It feeds the Incremental variation of ES (SES).

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ES (Scenario FX Rates)

Combine with [Booking].[Trades] to display trade-level input data by scenario.

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ES (Scenario PV)

Combine with [Booking].[Trades] to display trade-level input data by scenario.

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ES (Scenario PV Orig Ccy)

Combine with [Booking].[Trades] to display trade-level input data by scenario.

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ES Scenario Rank

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IMCC

Formula $IMCC = \omega \cdot IMCC( C )$ The measure is based on the unconstrained expected shortfall charges - ES (Capital Constrained) and Omega.

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IMCC.D2D

Formula $IMCC_{t}-IMCC_{t-1}$

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Omega

Formula $\omega=\rho +(1-\rho) \frac{ \sum_{i=1}^R IMCC(C_i) }{ IMCC(C)}$ The reference date is set with the hierarchy [Dates].[OmegaDate].[OmegaDate]. The measure is based on the weighted average of the constrained and unconstrained expected shortfall charges - ES (Capital Constrained) and ES (Capital Unconstrained). With $\omega$ IMCC formula can be rewritten as: $$IMCC = \omega \cdot IMCC( C )$$

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PnL Expand

Using this measure, you can display trade level input data of the ES calculation. We recommend combining this measure with the [Booking].[Trades] hierarchy. The [Risk].[Liquidity Horizons], [Risk].[Risk Classes] and [Risk].[Data Sets] hierarchies are also recommended.

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SES

Formula $SES = \sqrt{\sum_{i=1}^{I}ISES_{NM,i}^2}+\sqrt{\sum_{j=1}^{J}ISES_{NM,j}^2}+\sqrt{\left ( \rho \cdot \sum_{k=1}^{K}SES_{NM,k} \right )^2 + (1-\rho^2) \cdot \sum_{k=1}^{K}SES_{NM,k}^2}$ The measure is implemented as follows:

• for I_type non-modellable risk factors and J_type (non-modellable idiosyncratic credit risk factors) - it aggregates the squared stress scenario capital charges by risk factor (see ES (ISES)), then takes a square root,
• for K_type non-modellable risk factors, it computes the ES measure for each risk factor (see ES (SES)) and aggregates them with the prescribed correlation factor.

Use the Idiosyncratic hierarchy to break down the charge into idiosyncratic and non-idiosyncratic components and the Risk Classes hierarchy to display the risk factor’s risk class. Note that the SES measure disregards the actual capital treatment of individual positions. It computes charges as if all positions are under IMA. To limit the scope to positions officially under the “IMA” approach, apply a filter on FRTB Model equal to “IMA”.

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SES Differential

Computed using the same aggregation formula as SES, applied to ES (ISES) Differential and ES (SES) Differential instead of their base counterparts. It feeds the Incremental variation of SES.

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Squared ES (Liquidity Adj.)

Formula $ES^2 = \left(ES_T(P)\right)^2 + \sum_{j\geq 2}\left(ES_T(P,j)\sqrt{\frac{(LH_j - LH_{j-1})}{T}}\right)^2$

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Squared LHScaleFactor

Formula $\frac{(LH_j-LH_{j-1})}{T}$

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Squared LHScaleFactor Reference

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Technical

Technical measures supporting the Internal Model Approach (IMA) calculations.

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ES (base PV)

This measure is subtracted from the per-scenario PV vector to build the ES PnL vector.

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ES (base PV orig ccy)

This measure feeds ES (base PV).

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ES (PnL Vector) Modellable CCY

This measure feeds ES (Basic), PnL Expand, and ES Scenario Rank.

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ES (PnL Vector) Non-Modellable Idiosyncratic CCY

This measure feeds ES (PnL Vector) Non-Modellable Idiosyncratic and the idiosyncratic NMRF capital requirement, ES (ISES).

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ES (PnL Vector) Non-Modellable Non-Idiosyncratic CCY

This measure feeds ES (PnL Vector) Non-Modellable Non-Idiosyncratic and the non-idiosyncratic NMRF capital requirement, ES (SES).

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LH

LH only applies where the risk factor is modellable; it is used internally by the IMA calculations.

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Previous LH

This measure is used to compute Squared LHScaleFactor, which scales the ES calculation between consecutive liquidity-horizon buckets.