StressCalibration - Atoti Hub

The measures in this cube identify the stress periods by identifying the greatest IMCC and SES values over all 1-year periods since 2007.

ES (base PV) RAW

ima ES (base PV) RAW is a technical measure used internally by the stress calibration calculations. It is the base (day-0) portfolio valuation converted to display currency, feeding the ES P&L vector calculation.


Description	Technical measure

ES (Basic).Window

ima


Description	The measure performs expected shortfall aggregation for a set of return vectors
Required hierarchies	Risk Classes, Data Sets, Liquidity Horizons

When the Sliding Window hierarchy is not present, a vector of Expected Shortfalls is returned, which can be expanded on Sliding Window.

ES (Capital).Window

ima


Description	For each risk class and allin risk class, this is the expected shortfall charge across all sliding windows
Required hierarchies	Risk Classes
Reference
Formula	$\displaystyle ES = ES_{R,S} \cdot \frac{ES_{F,C}}{ES_{R,C}}$

The measure takes the result of the ES (Liquidity Adj.) measure filtered by [Risk].[Data Sets] equal to ‘Reduced Set Stressed’. It then scales that result by a ratio. The ratio is the ES (Liquidity Adj.) measure for [Risk].[Data Sets] equal to ‘Full Set Current’ divided by the ES (Liquidity Adj.) for the ‘Reduced Set Current’. 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). When the Sliding Window hierarchy is not present, a vector is returned, which can be expanded by bringing Sliding Window into the query.

ES (Capital Constrained).Window

ima


Description	The non-diversifiable risk class ES charges (also known as constrained expected shortfall charge)
Reference
Notation	$\sum_{i=1}^{R}{IMCC(C_i)} \text{ where } IMCC(C_i)=ES_{R,S,i} \cdot \frac{ES_{R,C,i} }{ES_{R,C,i} }$

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

ES (Capital Unconstrained).Window

ima


Description	The unconstrained expected shortfall charge
Reference
Notation	$IMCC(C)$
Formula	$\displaystyle IMCC(C)=ES_{R,S} \cdot \frac{ES_{F,C} }{ES_{R,C} }$

This measure represents expected shortfall liquidity-adjusted and scaled to stress period across risk classes. Also referred to as “unconstrained”.

ES (Current Ratio).Window

ima


Description	For each risk class and allin risk class, this is the ratio of the liquidity-adjusted ES for full current set and ES for reduced current set. It is floored at 1.
Required hierarchies	Risk Classes
Reference
Formula	$\displaystyle \max\left(\frac{ES_{F,C}}{ES_{R,C}},1\right)$

This measure gives the ratio of the liquidity-adjusted expected shortfall for the full current set to the expected shortfall for the reduced current set, per risk class and across all risk classes. The ratio is floored at 1.

ES (ISES).Window

ima


Description	The capital requirement for each non-modellable idiosyncratic risk factor (I-type risk factors and J-type risk factors), for each risk-factor, risk-class, and 1-year period.
Required hierarchies	Risk Classes, Risk Factors, Sliding Window
Reference

This measure shows the capital requirement for each non-modellable idiosyncratic risk factor (I-type risk factors and J-type risk factors), for each risk-factor, risk-class, and 1-year period.

ES (Liquidity Adj.).Window

ima


Description	Generic regulatory liquidity-adjusted ES measure for each Sliding Window
Required hierarchies	Risk Classes, Data Sets
Reference
Formula	$\displaystyle ES = \sqrt{\left(ES_T(P)\right)^2 + \sum_{j\geq 2}\left(ES_T(P,j)\sqrt{\frac{LH_j - LH_{j-1}}{T}}\right)^2}$

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. When the Sliding Window hierarchy is not present, a vector is returned, which can be expanded by bringing Sliding Window into the query.

ES (Model Variation).Window

ima For each risk class and the allin risk class, this measure gives the ratio of the liquidity-adjusted ES for the reduced current set to the ES for the full current set.


Description	For each risk class and allin risk class, this is the ratio of the liquidity-adjusted ES for reduced current set and ES for full current set
Required hierarchies	Risk Classes
Reference
Formula	$\displaystyle \frac{ES_{R,C}}{ES_{F,C}}$

ES (PnL Vector) Expand

ima


Description	P&L vector based on data set and sliding window analysis hierarchies expanded on scenario
Required hierarchies	Data Sets

This measure displays the ES Vector, based on the data set analysis hierarchy. To view the Reduced Set Stressed data set, the Sliding Window analysis hierarchy must be added.

ES (PnL Vector) Non-Modellable Non-Idiosyncratic

ima This measure provides the P&L vector for (non-Idiosyncratic) NMRFs, based on the sliding window analysis hierarchy expanded by scenario.


Description	P&L vector for (non-Idiosyncratic) NMRFs based on the sliding window analysis hierarchy expanded by scenario
Variations	rank
Required hierarchies	Scenario Dates, Risk Classes, Sliding Window

ES (PnL Vector) Non-Modellable Idiosyncratic

ima This measure provides the P&L vector for Idiosyncratic NMRFs, based on the sliding window analysis hierarchy expanded by scenario.


Description	P&L vector for Idiosyncratic NMRFs based on the sliding window analysis hierarchy expanded by scenario
Variations	rank
Required hierarchies	Scenario Dates, Risk Classes, Sliding Window

ES (Scenario FX Rates).Window

ima


Description	The FX rate applied under the stress scenario, used to convert the base-currency PV vector into the ES calculation currency, expanded across the scenario dimension
Required hierarchies	Data Sets

ES (Scenario PV).Window

ima


Description	The scenario-stressed portfolio valuation vector in display currency, expanded across the scenario dimension
Required hierarchies	Data Sets

ES (Scenario PV Orig Ccy).Window

ima


Description	The scenario-stressed portfolio valuation vector in original (booking) currency, expanded across the scenario dimension
Required hierarchies	Data Sets

ES (SES).Window

ima


Description	The capital requirement for non-modellable, non-idiosyncratic risk factors (K-type risk factors), for each risk-factor, risk-class, and 1-year period.
Required hierarchies	Risk Factors, Risk Classes, Sliding Window

IMCC.Window

ima


Description	The internally modeled capital charge, also known as aggregate capital charge for modellable risk factors across all sliding windows
Variations	euler, incremental
Reference
Notation	$IMCC$
Formula	$\displaystyle IMCC=\rho \left ( IMCC(C) \right )+(1-\rho) \left ( \sum_{i=1}^R IMCC(C_i) \right )$

The measure is based on the unconstrained expected shortfall charges - ES (Capital Constrained) and Omega. When the Sliding Window hierarchy is not present, a vector of indicators is returned, which you can expand on Sliding Window.

IMCC Indicator

ima


Description	Indicator is 1 when sliding window is equal to the max IMCC across all windows and 0 otherwise.
Variations	euler, incremental
Reference
Notation	$IMCC$
Formula	$\displaystyle IMCC=\rho \left ( IMCC(C) \right )+(1-\rho) \left ( \sum_{i=1}^R IMCC(C_i) \right )$

The measure is based on the weighted average of the constrained and unconstrained expected shortfall charges, ES (Capital Constrained) and ES (Capital Unconstrained). When the Sliding Window hierarchy is not present, a vector of indicators is returned, which you can expand on Sliding Window.

IMCC Max

ima


Description	The IMCC value of the sliding window flagged by IMCC Indicator, i.e. the maximum IMCC value across all sliding windows
Reference

This measure identifies the stress period used to calibrate the IMA: the sliding window whose IMCC value is the greatest across all windows since 2007.

LH.Window

ima LH is a technical measure used internally by the IMA calculations.


Description	Technical measure

Omega.Window

ima


Description	The IMCC multiplier reflecting weighted average of 1 and the ratio of undiversified IMCC(C) to diversified IMCC(C) (BCBS 395: 2.1 Q1) for each sliding window
Notation	$\omega$
Formula	$\displaystyle \omega=\rho +(1-\rho) \frac{ \sum_{i=1}^R IMCC(C_i) }{ IMCC(C)}$

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

, the IMCC formula can be rewritten as:

IMCC = \omega \cdot IMCC( C )

When the Sliding Window hierarchy is not present, a vector of indicators is returned, which you can expand on Sliding Window.

Previous LH.Window


Description	Technical

SES.Window

ima


Description	The stressed expected shortfall, for each risk-class and each 1-year period.
Variations	euler, incremental
Required hierarchies	Risk Classes, Sliding Window
Reference
Notation	$SES$
Formula	$\displaystyle SES = \sqrt{\sum_{i=1}^{I}ISES_{NM,i}^2}+\sqrt{\sum_{j=1}^{J}ISES_{NM,j}^2}+\sqrt{\left ( \rho \cdot \sum_{k=1}^{K}SES_{NM,k} \right )^2 + (1-\rho^2) \cdot \sum_{k=1}^{K}SES_{NM,k}^2}$

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.

The SES measure disregards the actual capital treatment of individual positions and 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”.

SES max

ima


Description	The most conservative SES values observed across all observation windows.
Variations	euler, incremental
Required hierarchies	Risk Classes, Sliding Window
Reference
Notation	$SES max$

When the Sliding Window hierarchy is not present, a vector of indicators is returned, which you can expand on Sliding Window.

Squared ES (Liquidity Adj.).Window

ima


Description	The expression under the root of the liquidity-adjusted expected shortfall formula
Reference
Formula	$\displaystyle ES^2 = \left(ES_T(P)\right)^2 + \sum_{j\geq 2}\left(ES_T(P,j)\sqrt{\frac{(LH_j - LH_{j-1})}{T}}\right)^2$

Squared LHScaleFactor.Window

ima


Description	The current liquidity horizon minus the previous and divided by the base liquidity horizon
Required hierarchies	Liquidity Horizons
Reference
Formula	$\displaystyle \frac{(LH_j-LH_{j-1})}{T}$

​ES (base PV) RAW

​ES (Basic).Window

​ES (Capital).Window

​ES (Capital Constrained).Window

​ES (Capital Unconstrained).Window

​ES (Current Ratio).Window

​ES (ISES).Window

​ES (Liquidity Adj.).Window

​ES (Model Variation).Window

​ES (PnL Vector) Expand

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

​ES (PnL Vector) Non-Modellable Idiosyncratic

​ES (Scenario FX Rates).Window

​ES (Scenario PV).Window

​ES (Scenario PV Orig Ccy).Window

​ES (SES).Window

​IMCC.Window

​IMCC Indicator

​IMCC Max

​LH.Window

​Omega.Window

​Previous LH.Window

​SES.Window

​SES max

​Squared ES (Liquidity Adj.).Window

​Squared LHScaleFactor.Window

ES (base PV) RAW

ES (Basic).Window

ES (Capital).Window

ES (Capital Constrained).Window

ES (Capital Unconstrained).Window

ES (Current Ratio).Window

ES (ISES).Window

ES (Liquidity Adj.).Window

ES (Model Variation).Window

ES (PnL Vector) Expand

ES (PnL Vector) Non-Modellable Non-Idiosyncratic

ES (PnL Vector) Non-Modellable Idiosyncratic

ES (Scenario FX Rates).Window

ES (Scenario PV).Window

ES (Scenario PV Orig Ccy).Window

ES (SES).Window

IMCC.Window

IMCC Indicator

IMCC Max

LH.Window

Omega.Window

Previous LH.Window

SES.Window

SES max

Squared ES (Liquidity Adj.).Window

Squared LHScaleFactor.Window