Demo IMA Approach

A sampled collection of requirements and approaches

Disclaimer: Data, charts and commentary displayed are for information purposes only and do not provide any advisory.

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Overview

• The Regulatory Context associated to Market Risk

• Basel IV - The Changes resulting from the FRTB

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The Regulatory Context associated to Market Risk

 

Basel IV - The Changes resulting from the FRTB

The Basel Committee of Banking Supervision (BCBS) published the Fundamental Review of Trading Book (FRTB) final rule to be incorporated under Basel IV. Implementations of Basel IV are performed by regulatory authorities such as FED, ECB/EBA and BOE/PRA with a deadline of January 2022.

The Basel Committee of Banking Supervision (BCBS) published the minimum capital requirements for market risk in January 2019 (rev. February 2019). This final rule regulatory text - commonly referred to as the Fundamental Review of Trading Book (FRTB) - replaces the previous minimum capital requirements for market risk.The FRTB amendments to the regulation is implemented in the EU in the revised Credit Risk Regulation (CRR 2).

Shown in the graph below are the components of FRTB split by Standardized (SA) and Internal Model Aproach (IMA).

 

The key changes introduced by the Fundamental Review of the Trading Book (FRTB) include

1. The separate computation of the Standardized Approach (SA) capital charge for each trading desk. The separate computation under SA must be performed regardless of any computation already performed under IMA. This paralleled computation becomes mandatory to ensure a fall-back is available. The SA charge is computed along the key components involved: the sensitivity based charge, the Regulatory Risk Add On (RRAO) and the Default Risk Charge (DRC).

• The Sensitivity Based Approach (SBA) accounts for linear and non-linear risk sensitivities and uses prescribed risk weights and correlation parameter

• The Residual Risk Add-On (SRSA) as a component within standardized accounts for linear and non-linear risk sensitivities

• The Default Risk Charge (DRC) as a component within standardized accounts for the credit risk in the trading book and uses prescribed risk weights and Basel parameter.

2. The introduction of the Espected Shortfall (ES) methodology as a replacement for VaR and sVaR;

• The Expected Shortfall metric, also sometimes referred to a conditional VaR, is defined as the expected loss given that the P&L exceeds the VaR at a 97.5% confidence level. According to Dowd (2005) - Measuring Market Risk, John Wiley & Sons - the ES metric can be interpreted as the average VaR for all confidence levels greater equal than the chosen one.

\[ES_{\alpha}(L)=\frac{1}{1-\alpha} \cdot \int_\alpha^1VaR_{\alpha}(L) d\alpha\]

• The replacement of VaR with Expected Shortfall is motivated by the preferable properties of the latter. In contrast to the VaR metric, the ES metric captures tail risks by accounting for the magnitude of losses that occur above the confidence level.

• Similar to the VaR approach, a scaling-up of the ES metric from the 1-day to the 10-day horizon can be performed and the ES metric must be calibrated to a period of market stress, i.e. the most stressed 12 month period based on the current portfolio. However, the identification of a suitable period of significant market stress can be based on a reduced set of risk factors, thereby reducing the complexity.

• Moreover, the demise of the VaR/sVaR model concept also impacts on the measurement of the Risks Not in the Model (RNIM). Non-Modellable Risk Factors (NMRF) should be excluded from the Expected Shortfall (ES) Model and should instead be subject to stress scenario implied capital requirements, i.e. a loss calibrated to the 97.5% confidence level over a period of extreme stress. The assessment of the modellability of risk factors is a separate requirement of the FRTB and set out in the CRR.

• Note that for a normal distributed Random Variable the following relationship between ES and VaR metrics holds \[ES_{0.975} = VaR_{0.99}\]

3. The classification of risk factors as modellable vs. non-modellable requires an assessment of modellability. Risk factors identified as non-modellable (NMFR) are capitalized under a Stress Scenario Risk Measure (SSRM). This ensures that only risk factors that are sufficiently liquid and observable are used for the Expected Shortfall (ES) calculation.

• The assessment of modellability of risk factors is performed quarterly in relation to criteria on the number of data points available for a certain risk factor. Precisely, 24 data points must be observable during the preceeding 12-month period, without any 90-day period with less than 4 data points.

• The risk factors in scope of the modellability assessment include Interest Rate curves, systematic and idiosyncratic factors pertaining to Equity multi-factor models, parameters pertaining to volatility surfaces etc.

• The identification of the stress scenario should be performed for each non-modellable risk factor.

• Risk factors classified as of the NMRF type are subjected to a Stress Scenario Risk Measure (SSRM). Precisely, the SSRM is the loss resulting from applying the stress scenario to that risk factor. As a consequence a separate capital charge is applied to all non-modellable risk factors which is typically based on a Stressed Expected Shortfall (SES).

4. The introduction of additional Liquidity Horizons to replace the uniform 10-day holding period horizon used under Basel 3

• The new Liquidity Horizons replace the old 10-day horizon across all risk factors. As a result, the regulatory capital becomes more dear for risk factors associated to larger horizons (> 10 days)

• Liquidity Horizons range from 10 to 120 days depending on the complexity of the asset type. Shown belown for illustration are different horizons as pertaining to various asset classes.

	Liquidity Horizon (days)
Equity Volatility	20
Interest Rate Volatility	40
Credit Spread Volatility (HY)	60

 

5. The replacement of the Incremental Risk Charge (IRC) model by the Default Risk Charge (DRC) model. The DRC model captures the default of individual issuers as well as the simultaneous default of multiple issuers and computes the market value impact of those defaults on the debt and equity positions in the trading book.

6. The application of a more rigorous model approval process at the trading desk level.

7. The strenghtening of data integrity is highlighted by the introduction of the concept of modellable vs. non-modellable risk factors. A risk factor qualifies for being modellable if the data used for calibration have more than 24 data points per year (with a maximum period of one month between consecutive months). Capitalization of non-modellable risk factors is performed under a stress scenario and diversification (correlation) effects are not permitted.

 

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The Requirement of VaR and SVaR Methodologies

Requirements on VaR and SvaR methodologies and model operation are set out in the Capital Requirements Regulation (CRR) Article 365 and 367. Among these requirements are specific demands on data inputs and data quality, as well as model assuptions and proxies:

• Assumptions related to risk factors and their distributions are expected to be shown appropriate on market data;

• Appropriateness of risk factors used for VaR/sVaR calculation should be satisfactory in terms of numbers of factors that reconcile with pricing and economic P&L by means of an inventorized mapping;

• Appropriateness of pricing methods used for VaR/sVaR calculation should be satisfactory in terms of a reconciliattion with the pricing methos used for economic P&L;

• For Monte Carlo simulations it is important to ensure a sufficient number of simulation runs to allow the production of precise and stable Var / sVaR figures;

• The risk factor times series used to input the VaR / sVaR models are expected to be of sufficient data quality covering the extent of missing and replaced data and estblishing a documentation on the methodoldogy used for filling missing data. OUtliers in data should not be replaced unless there is convincing case of erroneous data.

• For proxies used in VaR/sVaR calculation the recognition of valid approaches rests on the use of standard methods, e.g. the use of beta for equity returns, and the consistency of market data used for pricing (economic P&L) vis-a-vis the actual and hypothetical P&L. In this regards, transparency should be provided on the number of proxied time series;

 

The Backtesting Requirements

Note that a regulatory multiplication factor is used to establish a direct link between the number of outliers and the capital requirements. This way, the regulatory capital requirements are dependent on the model’s adequacy.

In a nutshell, backtesting compares the daily 99%-VaR against each of the hypothetical P&L and the actual P&L measured over the historical 1-year horizon. Note that the hypothetical P&L is calculated based on unchanged positions and obtained by revaluing the positions at the end of the previous day using the market data at the end of the current day. hence, P&L changes due to new positions and intraday trading are not accounted for and the emphasis is put on the change in risk factors.

By contrast, actual P&L is obtained from actual market data of the current day, including profits and losses from intraday trading but excluding commissions, valution adjustments and Net Interest Income.

The exceptions are measured as the outliers that exceed the daily VaR of either the hypothetical or actual loss at a certain day.The counting of exceptions applied to backtesting uses the greater number of either the hypothetical or the actual exceptions.

An overall objective of backtesting is to provide confidence that the VaR model adequately accounts for the instrument level volatility and the correlations.

CRR regulations as set out in CRR Articles 106 (3), 352 (2), 366 and 386 include a definition of the historical data period to be used for backtesting. Backtesting of VaR limits is mandatory an exercise for both hypothetical and actual P&L (cf. CRR Article 366 (3)).

The CRR requirements point out that

• Backtesting should be based on the number of VaR overshootings over the most recent past of 250 business days. For this, the recognition of any overshooting should be based on a comparison of overshootings on hypothetical and and actual changes and the higher number should be used;

• The recognition of VaR overshootings (exceptions) should be complemented by a rigorous analysis of the reasons involveld, e.g. portfolio analysis to identify positions and market moves responsible and model analysis to identify model shortcomings,

• Documentation on policies and procedures should exists to explain the calculation details of actual & hypothetical P&L and how these differ;

• The actual P&L used must be before fees and Net Interest Income and should use the same pricing and model configurations as used for calculation of economic P&L. Furthermore that Credit, Debt Valuation and Addional Valuation Adjustment (AVA) should be disregarded for the calculation of actual P&L but that all other valuation adjustments should be included. Finally that values changes due to counterparty default should be out-of-scope for calculation of actual P&L;

• The hypothetical P&L on the other hand has to emphasis the change of risk factors only, and is calculated based on unchanged trading positions (disregarding any intraday change in positions or any new positions over the past day) with any valution adjustments being out-of-scope;

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The Requirements of the IRC Methodology

The Incremental Risk Charge (IRC) is the risk charge associated with the default and migration risk of trading book positions excluding securitisations.

Note that with effect of implementing FRTB requirements, the IRC is required to be overriden by the Default Risk Charge (DRC).

 

• The Incremental Risk Charge (IRC) is a one-year VaR at the 99.9% confidence level devised to measure the Credit Risk in the Trading Book. Its purpose is to capture losses due to credit migrations and defaults in the Trading Book;

• The IRC approach is based on the simulation of asset returns over a 1-year horizon using a multi-period model. A multi-period model is required to account for intra-year liquidity horizons and for a rebalancing of the portfolio, i.e. replacing deteriorated credit risky instruments at the end of their liquidity horizons to roll back to a constant level of risk;

• Parameter inputs to the model required include a correlation matrix of asset returns based on historical data and asset return thresholds obtained from a suitable credit migration matrix;

• The minimum liquidity horizon permitted is 3 months. Typically, longer liquidity horizons are assigned to securities of comparatively worse credit quality.

• A scenario generator is used to simulate the value change of each position at their respective liquidity horizons. Given that a rebalancing occurs for those postions defaulted or migrated in the scenario, a total value change a total value change needs to be calculated across positions over the one-year horizon. The total value change simulated for each position in the scenario is calculated by compounding the respective value changes at the liquidity horizons up to the one-year horizon. The distribution of portfolio value changes is thus available from the generation of a sufficient number of scenarios;

• Regulatory expectations on the opeation and maintance of te IRC Model include that the number of simulations used is adequate to provide an accurate estimate of the charge. A confidence interval surrounding the IRC estimate should be provided to provide disclosure on the statistical errror. Bespoke Transition Matrices for Sovereigns and other type of issuers should be used. The Factor Model should consist of two kinds of systematic factors and the Correlation Matrix should be quantified based on market data. Finally, the estimates used for PDs and Recoveries should be primarily based on the banks own IRB measures, and a hierarchy of sources should be established and consistently applied to avoid cherry picking.

 

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The Requirements on the Risks Not in the Model (RNIM)

The Risks not in Model (RNIM) is the risk charge associated to risks not considered in the internal model. Precisely this covers any risks not modelled in the internal model and any risks where the data issues prevent any modelling.

Reasons for risks not captured by VaR, SVaR and IRC model categories can include data issues (e.g. non-availability) or that certain risks can’t be modelled. The quantification of RNIM should be commensurate with the loss in each category (10day 99% VaR, 10 day 99% SVaR, 1year 99.9% IRC). CRR regulations on Risks not in the Model are set out in the articles 367 and 369.

 

• The identification of RNIM is required to be an integrated element of the new product approval process and the backtesting / validation process;

• The measurement of RNIM is required to quantify the impact of RNIV on VaR/sVaR or IRC on a standalone and on a total basis without considering diversification effects;

• A monitoring of RNIV should be established and performed regularly;