IMA

This section describes how requirements in BCBS 457 are implemented in Atoti FRTB (Internal Models Approach). For further details, see the Internal Models Approach. The formulae and definitions in the BCBS document are not repeated here – instead, references are provided to the relevant paragraphs, as appropriate.

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Calculation steps

The aggregated internal models-based capital charges for IMA desks in green or amber PLA zones is given as: [MAR33] $IMA_{GA} = C_A + DRC$ where $C_A = max\left\{ IMCC_{t-1} + SES_{t-1};\ m_c \cdot IMCC_{avg} + SES_{avg} \right\}$

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Expected Shortfall (ES)

Atoti FRTB can calculate Expected Shortfall (ES). The Solution requires P&L vectors as inputs that are keyed by the following attributes:

• AsOfDate
• TradeId
• Dataset (ES_rs, ES_fc, ES_rc)
• Risk Class
• Liquidity Horizon
• Currency

For information, see the input file format for Expected Shortfall PL Trade.   Atoti FRTB allows the ES percentile to be expressed as a context value with a default setting of 97.5 Atoti FRTB contains measures for the calculation of the following. The calculation chain exposes the intermediate measures for:

• Raw input data on a drill through panel and / or pivot view
• Conversion of input P&L vectors to a reference currency (if the source systems provide native currency P&L values)
• Calculation of ES (liquidity adjusted, capital constrained and capital unconstrained)
• Squared Liquidity Horizon (LH) factor and
• IMCC

  Atoti FRTB calculates the three Expected Shortfall values for ES_rs, ES_fc and ES_rc separately and also applies the risk capital adjustment. Atoti FRTB assumes that data for ES_rs has been supplied as an input. For information on how Atoti FRTB can help with the assessment of the ES period of stress, see Evaluating the ES Period of Maximum Stress.  

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Internally Modelled Capital Charge (IMCC)

The rho factor in the IMCC calculation is parameterized which allows the user to configure the factor at query time. Part of the IMCC calculation for the aggregated charge requires the weighted average charge per desk over the last 60 days. Atoti FRTB does not calculate this value. It is required as desk-level input data to the Solution.

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Stressed Capital Add-On (SES)

In the IMARiskFactors store, Atoti FRTB uses the Non-Modellable Risk Factors (NMRFs) and Idiosyncratic fields to distinguish between three types of risk factors:

• Modellable
• Non-modellable, but not idiosyncratic
• Non-modellable idiosyncratic credit spread risk factors that have been demonstrated to be appropriate to aggregate with zero correlation

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Default risk charge for IMA (DRC)

Atoti FRTB presents a VaR-based approach to DRC for IMA which is calculated from P&L vectors at trade level. The result is required at 99.9% which means that the input vectors are typically of size 100,000 or more. The input vector at the trade level is very sparse (meaning that most of the million elements are zero). This is because any one obligor is insensitive to most of the scenarios. Atoti FRTB compresses the sparse vectors and stores them in off-heap memory so that the trade level vectors use the minimum possible memory. Atoti FRTB provides a context value that enables the user to look at the IMA DRC under different confidence levels. By default, Atoti FRTB computes the IMA DRC at 99.9% but a context value is provided that enables the user to work with other levels.

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Evaluating the ES Period of Maximum Stress

Atoti FRTB does not provide the scheduling tasks required to load the data for this calculation. The vector corresponding to the stressed period can be written out to a CSV file by Atoti FRTB.

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P&L Attribution Tests and Backtesting

There are two cubes:

• The PL Summary Cube for the desk and firm-wide monitoring.
• The PL Cube for trade level analytics, including aggregating VaR P&L vectors to the desk level and calculating the VaR values.

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Supported Use Cases

The P&L Attribution Tests and Backtesting have been designed to enable the following use cases.

1. Monitoring historical VaR and P&L values at the desk and firm-wide levels, as required by regulation.
2. Calculating desk and firm-wide VaR values from trade level VaR P&L vectors.
3. Customizing trade level inputs and analytics to support analyzing recent exceptions/outliers.

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PL Summary Cube

The PL Summary Cube collects aggregated data with a long history (at least the 1 year required by the regulations) at the desk and firm-wide levels. Including:

• Daily P&L values (actual, hypothetical, and risk-theoretical).
• Daily VaR values at the 97.5% and 99% confidence level.

The cube includes the analytics required for P&L Attribution Tests and Backtesting. Including:

• The mean of the difference between the risk-theoretical and hypothetical P&L (unexplained P&L) divided by the standard deviation of the hypothetical P&L.
• The variance of the unexplained P&L divided by the variance of the hypothetical P&L.
• A count of the number of exceptions when comparing the Actual P&L and Hypothetical P&L against the VaR at the 97.5% and 99% confidence levels.

For more information, see Cubes.
The input data to the summary cube requires the following data fields in the input data files:

• AsOfDate
• Desk name
• Currency
• Actual PL
• Hypothetical PL
• Theoretical PL
• VaR 99
• VaR 97.5

For information, see the input file format for PL Summary.

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PL Cube

The PL Cube collects recent data at the trade (or position) level, including the VaR P&L vectors.

• Includes VaR calculations, for calculating the desk and firm-wide VaR values at the 97.5% and 99% confidence level.
• It is expected that this cube will be customized to support analyzing exceptions/outliers.

For more information, see Cubes.

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IMA Multiplier

The IMA Multiplier factors are held in a datastore so that they can be fetched at query time and can be sensitive to jurisdiction. Atoti FRTB provides a post-processor that can take as input the number of P&L/VaR exceptions (see P&L Attribution Tests and Backtesting) and return a multiplier factor as a measure.