PL - Atoti Hub

model_eligibility Measures for the PL Attribution Test (PLAT) and Backtesting, used to assess the eligibility of a desk for the Internal Model Approach.

Actual PL


Description	A sum of Actual PL input values
Reference

Actual PL Lookback


Description	The historical Actual PL values
Required hierarchies	Lookback

Actual PL Lookback Rank


Description	Technical measure
Required hierarchies	Lookback

Actual PL Lookback Index


Description	Technical measure
Required hierarchies	Lookback

Exception 97.5 (Actual) Lookback


Description	The historical Exception 97.5 (Actual) values
Required hierarchies	Lookback

The measure helps to inspect exceptions for PLAT and Backtesting.

You can change the lookback horizon (for instance 1M) to a shorter or longer observation window using the NbDaysPLMeasures context value.

Exception 97.5 (Hypothetical) Lookback


Description	The historical Exception 97.5 (Hypothetical) values
Required hierarchies	Lookback

The measure helps to inspect exceptions for PLAT and Backtesting.

You can change the lookback horizon (for instance 1M) to a shorter or longer observation window using the NbDaysPLMeasures context value.

Exception 99 (Actual) Lookback


Description	The historical Exception 99 (Actual) values
Required hierarchies	Lookback

The measure helps to inspect exceptions for PLAT and Backtesting.

You can change the lookback horizon (for instance 1M) to a shorter or longer observation window using the NbDaysPLMeasures context value.

Exception 99 (Hypothetical) Lookback


Description	The historical Exception 99 (Hypothetical) values
Required hierarchies	Lookback

The measure helps to inspect exceptions for PLAT and Backtesting.

You can change the lookback horizon (for instance 1M) to a shorter or longer observation window using the NbDaysPLMeasures context value.

Hypothetical PL


Description	A sum of Hypothetical PL input values
Reference

Hypothetical PL Lookback


Description	The hypothetical PL contributing to the eligibility statistics calculations
Required hierarchies	Lookback

The measure helps to inspect actual contributors to the eligibility statistics calculations and spot potential data quality issues, such as spikes or missing values.

You can change the lookback horizon (for instance 1M) to a shorter or longer observation window using the NbDaysPLMeasures context value.

Hypothetical PL Lookback Rank


Description	Computes hypothetical PL rank for each observation date
Required hierarchies	Lookback

Hypothetical PL Lookback Index


Description	Technical measure
Required hierarchies	Lookback

Kolmogorov-Smirnov Test Metric


Description	The Kolmogorov Smirnov statistics
Reference

Kolmogorov-Smirnov Test p-value


Description	The p-value for the Kolmogorov-Smirnov Test.
Reference

Mean Ratio


Description	The mean of the unexplained P&L divided by the standard deviation of the hypothetical P&L (BCBS 352: 183 (b))

The mean ratio is a P&L attribution test metric, computed as shown below. Mean Ratio = Mean Unexplained PL / Std Dev Hypothetical PL

Mean Unexplained PL


Description	The mean of the unexplained P&L (BCBS 352: 183 (b))

This page describes the Mean unexplained PL measure, which provides the mean of the unexplained P&L. The measure is computed based on the Unexplained PL measure.

p-value (Actual) Lookback


Description	The historical p-value (Actual) values
Required hierarchies	Lookback

p-value (Actual) Lookback Rank


Description	Technical measure
Required hierarchies	Lookback

p-value (Actual) Lookback Index


Description	Technical measure
Required hierarchies	Lookback

p-value (Hypothetical) Lookback


Description	The historical p-value (Hypothetical) values
Required hierarchies	Lookback

p-value (Hypothetical) Lookback Rank


Description	Technical measure
Required hierarchies	Lookback

p-value (Hypothetical) Lookback Index


Description	Technical measure
Required hierarchies	Lookback

PL Scenario Rank


Description	Simulated PL rank for each VaR Scenario
Required hierarchies	Scenarios

Spearman Correlation Metric

This page describes the Spearman correlation metric measure, which provides the Spearman correlation statistics.


Description	The Spearman Correlation statistics
Reference

Spearman Correlation Metric Denominator


Description	Technical measure

Spearman Correlation Metric Numerator


Description	Technical measure

Std Dev Hypothetical PL


Description	The standard deviation of hypothetical PL
Reference
Formula	$\displaystyle stdev = \sqrt{\frac{\sum(x - \bar{x})^2}{n}}$

The measure is computed based on the Hypothetical PL measure.

Std Dev Hypothetical PL Lookback Rank


Description	Technical measure

Std Dev Theoretical PL Lookback Rank


Description	Technical measure

Theoretical PL


Description	A sum of Theoretical PL input values (BCBS 352: 183)

Theoretical PL Lookback


Description	The theoretical PL contributing to the eligibility statistics calculations
Required hierarchies	Lookback

The measure helps to inspect the actual contributors to the eligibility statistics calculations and spot potential data quality issues, such as spikes or missing values.

The lookback horizon (for instance 1M) can be changed to a shorter or longer observation window using the NbDaysPLMeasures context value.

Theoretical PL Lookback Rank


Description	Computes risk-theoretical PL rank for each observation date
Required hierarchies	Lookback

Theoretical PL Lookback Index


Description	Technical measure
Required hierarchies	Lookback

Unexplained PL


Description	Difference between Risk Theoretical PL and Hypothetical PL

Unexplained PL Lookback


Description	Unexplained PL contributing to the eligibility statistics calculations (BCBS 352: 183)
Required hierarchies	Lookback

The measure helps to inspect actual contributors to the eligibility statistics calculations and spot potential data quality issues, such as spikes or missing values.

The lookback horizon (for instance 1M) can be changed to a shorter or longer observation window using the NbDaysPLMeasures context value.

Variance Hypothetical PL

This page describes the Variance hypothetical PL measure, which provides the variance of the hypothetical P&L (BCBS 352: 183 (b)).


Description	The variance of the hypothetical P&L (BCBS 352: 183 (b))
Formula	$\displaystyle \frac{\sum (x-\bar{x})^2}{n}$

Variance Ratio

This measure gives the variance of the unexplained P&L divided by the variance of the hypothetical P&L.


Description	The variance of the unexplained P&L divided by the variance of the hypothetical P&L (BCBS 352: 183 (b))

Variance Unexplained PL

This measure gives the variance of the unexplained P&L.


Description	The variance of the unexplained P&L (BCBS 352: 183 (b))
Formula	$\displaystyle \frac{\sum (x-\bar{x})^2}{n}$

VaR

ES 97.5

This measure provides the trade-level 1-day expected shortfall at the 97.5% confidence level.


Description	The trade level 1-day expected shortfall at 97.5% confidence level

ES 99

This measure provides the expected shortfall at the 99% confidence level.


Description	The expected shortfall at 99% confidence level

Exception 97.5 (Actual)


Description	The measure returns 1 if Actual PL is below VaR 97.5 (previous day).
Reference

Exception 97.5 (Actual) Count


Description	The rolling sum of Exception 97.5 (exceptions from Actual)
Reference

Exception 97.5 (Actual) Dates


Description	The list of past dates where Actual PL overshoots VaR
Reference

Exception 97.5 Count


Description	The max of Exception 97.5 (Actual) and Exception 97.5 (Hypothetical)
Reference

Exception 97.5 (Hypothetical)


Description	The measure returns 1 if Hypothetical PL is below VaR 97.5 (previous day).
Reference

Exception 97.5 (Hypothetical) Count


Description	The rolling sum of Exception 97.5 (exceptions from Hypothetical)
Reference

Exception 97.5 (Hypothetical) Dates


Description	The list of past dates where Hypothetical PL overshoots VaR
Reference

Exception 99 (Actual)


Description	The measure returns 1 if Actual PL is below VaR 99 (previous day).
Reference

Exception 99 (Actual) Count


Description	The rolling sum of Exception 99 (exceptions from Actual)
Reference

Exception 99 (Actual) Dates


Description	The list of past dates where Actual PL overshoots VaR
Reference

Exception 99 Count


Description	The max of Exception 99 (Actual) and Exception 99 (Hypothetical)
Reference

Exception 99 (Hypothetical)


Description	The measure returns 1 if Hypothetical PL is below VaR 99 (previous day).
Reference

Exception 99 (Hypothetical) Count


Description	The rolling sum of Exception 99 (exceptions from Hypothetical)
Reference

Exception 99 (Hypothetical) Dates


Description	The list of past dates where Hypothetical PL overshoots VaR
Reference

Outlier 97.5

This measure returns the maximum of the actual and hypothetical 97.5 exceptions used for model eligibility.


Description	Max of (Exception 97.5 (Actual), Exception 97.5 (Hypothetical))

Outlier 97.5 Count


Description	The rolling sum of Outlier 97.5
Reference

Outlier 97.5 Dates


Description	The list of past dates where Actual PL or Hypothetical PL overshoots VaR
Reference

Outlier 99


Description	Max of (Exception 99 (Actual) , Exception 99 (Hypothetical))

Outlier 99 Count


Description	The rolling sum of Outlier 99
Reference

Outlier 99 Dates


Description	The list of past dates where Actual PL or Hypothetical PL overshoots VaR
Reference

p-value (Actual)


Description	The actual PL p-value from upstream system (BCBS 352: 183)

p-value (Hypothetical)


Description	The hypothetical PL p-value from upstream system (BCBS 352: 183)

VaR 97.5% (Previous Day)


Description	The measure ‘VaR 97.5%’ taken as of previous day. This measure is tested against PL time series.
Reference

VaR 97.5% (previous day) Lookback


Description	The historical VaR 97.5% (previous day) values
Required hierarchies	Lookback

VaR 99% (Previous Day)


Description	The measure ‘VaR 99%’ taken as of previous day. This measure is tested against PL time series.
Reference

VaR 99% (previous day) Lookback


Description	The historical VaR 99% (previous day) values
Required hierarchies	Lookback

VaR PL


Description	Technical measure holding the VaR PL Vector, which can be expanded using the `VaR PL Expand` measure.

VaR PL Expand


Description	The simulated PL vectors - input data for the VaR calculation
Required hierarchies	Scenarios