BIPRU 7.10 Use of a Value at Risk Model
Application
BIPRU 7.10 applies to a firm with a VaR model permission.
Introduction and purpose
BIPRU 7.10 provides details of when the FSA expects to allow a firm to use a VaR model (value at risk model) for the purpose of calculating part or all of its PRR. It introduces the concept of a VaR model, the methodology behind it and the link to the standard market risk PRR rules. It then goes on to detail the application and review process. The bulk of BIPRU 7.10 specifies the model standards and risk management standards that firms will be required to meet in order to use a VaR model. It further stipulates requirements for stress testing, backtesting, capital calculations and finally the reporting standards expected by the FSA.
The models described in BIPRU 7.10 are described as VaR models in order to distinguish them from CAD 1 models, which are dealt with in BIPRU 7.9 (Use of a CAD 1 model). A VaR model is a risk management model which uses a statistical measure to predict profit and loss movement ranges with a confidence interval. From these results PRR charges can be calculated. The standards described in BIPRU 7.10, and which will be applied by the FSA, are based on and implement Annex V of the Capital Adequacy Directive.
The aim of the VaR model approach is to enable a firm with adequate risk management systems to be subject to a PRR requirement that is more closely aligned with the risks to which it is subject than the PRR requirements generated by the standard market risk PRR rules. This provides a firm with an incentive to measure market risks as accurately and comprehensively as possible. It is crucial that those responsible for managing market risk at a firm should be aware of the assumptions and limitations of the firm's VaR model.
There are a number of general methodologies for calculating PRR using a VaR model. The FSA does not prescribe any one method of computing VaR measures. Moreover, it does not wish to discourage any firm from developing alternative risk measurement techniques. A firm should discuss the use of any alternative techniques used to calculate PRR with the FSA.
A firm should not use the VaR model approach to calculate PRR unless it has a VaR model permission. If a firm does not have such a permission it should use the standard market risk PRR rules. Therefore, a firm needs to apply for a VaR model permission in order to calculate its PRR using a VaR model instead of (or in combination with) the standard market risk PRR rules.
Conditions for granting a VaR model permission
A waiver or other permission allowing the use of models in the calculation of PRR will not be granted if that would be contrary to the Capital Adequacy Directive and any VaR model permission which is granted will only be granted on terms that are compatible with the Capital Adequacy Directive. Accordingly, the FSA is likely only to grant a waiver or other permission allowing the use of models in the calculation of PRR if it is a VaR model permission or a CAD 1 model waiver.
BIPRU 7.10 sets out the minimum standards that the FSA expects firms to meet before granting a VaR model permission. The FSA will not grant a VaR model permission unless it is satisfied that the requirements of BIPRU 7.10 are met and it is satisfied about the procedures in place at a firm to calculate the model PRR. In particular the FSA will not normally grant a VaR model permission unless it is satisfied about the quality of:
- (1)
the internal controls and risk management relating to the VaR model (see BIPRU 7.10.56G - BIPRU 7.10.82R);
- (2)
the VaR model standards (see BIPRU 7.10.24R-BIPRU 7.10.55G); and
- (3)
stress testing and backtesting procedures relating to a VaR model (see, in addition to (2), BIPRU 7.10.83R - BIPRU 7.10.112G).
The FSA recognises that the nature of VaR models will vary between firms. The scope of and the requirements and conditions set out in a VaR model permission may therefore differ in substance or detail from BIPRU 7.10 in order to address individual circumstances adequately. However any differences will only be allowed if they are compliant with the Capital Adequacy Directive. A VaR model permission will implement any such variation by modifying BIPRU 7.10. A VaR model permission may also include additional conditions to meet the particular circumstances of the firm or the model.
The VaR model permission application and review process
Details of the general process for applying for a VaR model permission are set out in BIPRU 1.3 (Applications for advanced approaches). Because of the complexity of a VaR model permission, it is recommended that a firm discuss its proposed application with its usual contact at the FSA before it makes the application.
In order for a VaR model permission to be granted, the FSA is likely to undertake a review to ensure that it is adequate and appropriate for the PRR calculation.
The VaR model review process may be conducted through a series of visits covering various aspects of a firm's control and IT environment. Before these visits the FSA may ask the firm to provide some information relating to the firm's VaR model permission request accompanied by some specified background material. The VaR model review visits are organised on a timetable that allows the firm being visited sufficient time to arrange the visit and provide the appropriate pre-visit information.
As part of the process for dealing with an application for a VaR model permission the following may be reviewed: organisational structure and personnel; details of the firm's market position in the relevant products; revenue and risk information; valuation and reserving policies; operational controls; information technology systems; model release and control procedures; risk management and control framework; risk appetite and limit structure; future developments relevant to model recognition.
The FSA may complement its own review of a VaR model permission request with one or more reviews by a skilled person under section 166 of the Act (Reports by skilled persons). Such a review may also be used where a VaR model permission has been granted to ensure that the requirements BIPRU 7.10 and of the VaR model permission continue to be met.
Conditions for a VaR model outside the United Kingdom
Where a VaR model used outside the United Kingdom differs from that used in the United Kingdom the FSA may request details of the reasons for using different models.
Scope of VaR models
A firm must use the VaR model approach to calculate the PRR for a position:
- (1)
to the extent that the risks in relation to that position are within the scope of the VaR model permission (see BIPRU 7.10.136R (Link to standard PRR rules: Incorporation of the model output into the capital calculation)); and
- (2)
if the position is of a type that comes within the scope of the VaR model permission.
In accordance with BIPRU 7.10.18R (1) a VaR model permission will set out the risk categories that it covers, which are expected to be one or more of the following types:
- (1)
interest rate general market risk;
- (2)
interest rate specific risk (in conjunction with interest rate general market risk);
- (3)
- (4)
equity specific risk (in conjunction with equity general market risk);
- (5)
CIU risk;
- (6)
foreign currency risk; and
- (7)
commodity risk.
A VaR model permission will generally set out the broad classes of position within its scope. It may also specify how individual products within one of those broad classes may be brought into or taken out of the scope of the VaR model permission.
The broad classes of position referred to in BIPRU 7.10.20G are as follows:
- (1)
linear products, which comprise securities with linear pay-offs (e.g. bonds and equities) and derivative products which have linear pay-offs in the underlying risk factor (e.g. interest rate swaps, FRAs, total return swaps);
- (2)
European, American and Bermudan put and call options (including caps, floors and swaptions) and investments with these features (see BIPRU 7.6.18R (Table: Option PRR: methods for different types of option) for an explanation of some of these terms);
- (3)
Asian options, digital options, single barrier options, double barrier options, look back options, forward starting options, compound options and investments with these features (see BIPRU 7.6.18R for an explanation of some of these terms); and
- (4)
all other option based products (e.g. basket options, quantos, outperformance options, timing options) and investments with these features (see BIPRU 7.6.18R for an explanation of some of these terms).
The categorisation described in BIPRU 7.10.21G may be amended or replaced in the case of a particular firm's VaR model permission.
Model standards: General
A firm must comply with the minimum standards set out in BIPRU 7.10.26R - BIPRU 7.10.53R in calculating the model PRR.
The FSA accepts that the scope and nature of VaR models varies across firms. This means that different firms are likely to calculate different estimates of market risk for the same portfolio. Systematic differences are due to length of data series, choice of methodology (historical or Monte Carlo simulation or variance-covariance method or a hybrid of these), differences in aggregating risks within and across broad risk factors, the treatment of options and other non-linear products and the specification of risk factors.
Model standards: Frequency of calculations and confidence level
The model PRR must be computed at least once every business day, using a 99% one-tailed confidence limit.
A firm may meet the requirement in BIPRU 7.10.26R by using different model parameters and employing a suitable adjustment mechanism to produce a figure which is equivalent to the figure produced using the parameters set out in BIPRU 7.10.26R. For example, a firm's model may use a 95% one-tailed confidence limit if the firm has a mechanism to convert the output of the model to reflect a 99% one-tailed confidence limit.
Model standards: Holding period
In calculating the VaR number, a firm must either use a ten business day holding period, or use a holding period converted to a ten business day holding period. However if the firm's VaR model permission specifies that the firm must use a specific method, the firm must do so.
If a firm uses a holding period other than 10 business days and converts the resulting VaR measure to a ten business day equivalent measure, it should be able to justify the choice of conversion technique. For example, the square root of time method will usually be justifiable. The FSA considers it good practice ultimately to move towards the application of an actual ten business day holding period, rather than using different holding periods.
Model standards: Observation period
Subject to BIPRU 7.10.31R, the calculation of VaR numbers must be based on an effective historical observation period that is the longest possible consistent with a prudent VaR number. That period must be at least one year or such longer period as may be set out in the firm's VaR model permission. However if using that prescribed observation period does not result in a sufficiently prudent way of calculating a VaR measure or a component of a VaR measure the firm must shorten this observation period until the observation period is consistent with a prudent VaR number.
Model standards: Data series
A firm must ensure that the data series used by its VaR model is reliable. Where a reliable data series is not available, proxies or any other reasonable value-at-risk measurement technique must be used. A firm must be able to demonstrate that the technique is appropriate and does not materially understate the modelled risks.
A data series is unreliable if it has, for example, missing data points, or data points which contain stale data. Reliable data series may be difficult to obtain for new products (for example an instrument of longer dated tenor that did not previously trade) and for less liquid risk factors or positions. With regard to less liquid risk factors or positions, a firm may use a combination of prudent valuation techniques and alternative VaR estimation techniques to ensure there is a sufficient cushion against risk over the close out period which takes account of the illiquidity of the risk factor or position.
- (1)
If a weighting scheme or other similar method is used to calculate VaR numbers, then the effective observation period must be at least one year. Where a weighting scheme is used, the weighted average time lag of the individual observations must not be less than six Months.
- (2)
If a specific observation period or weighted average time lag is specified in a firm's VaR model permission, the firm must comply with that if it is longer than the period specified in (1).
- (3)
However, if a weighting scheme in (1) or (2) would result in imprudent VaR numbers then the weighting scheme must be adjusted so that it is consistent with a prudent VaR number.
A firm must update data sets in accordance with the frequency set out in its VaR model permission. If volatility in market prices or rates necessitates more frequent updating in order to ensure a prudent calculation of the VaR measure the firm must do so.
The minimum updating frequency that can be specified in a VaR model permission is quarterly.
Model standards: Aggregation across risk categories
The process for determining and implementing correlations within and across risk categories must be sound, implemented with integrity and consistent with the terms of the firm's VaR model permission.
In aggregating VaR measures across risk or product categories, a firm must not use the square root of the sum of the squares approach unless the assumption of zero correlation between these categories is empirically justified. If correlations between risk categories are not empirically justified, the VaR measures for each category must simply be added in order to determine its aggregate VaR measure. But to the extent that a firm's VaR model permission provides for a different way of aggregating VaR measures:
Model standards: Risk factors: Introduction
Subject to BIPRU 7.10.53R (Model standards: Materiality), a VaR model should capture and accurately reflect all material risks arising on the underlying portfolio on a continuing basis insofar as those risks are within the scope of the VaR model permission. This should encompass general market risk and, to the extent that this comes within the scope of the VaR model permission, specific risk. A firm should ensure that the VaR model has sufficient risk factor granularity to be able to capture all such material risks and that these are properly documented and specified.
Model standards: Risk factors: General
In the case of general market risk and risks with respect to which the standard market risk PRR rules do not distinguish between general market risk and specific risk, a firm's VaR model must capture a sufficient number of risk factors in relation to the level of activity of the firm and in particular the risks set out in BIPRU 7.10.40R - BIPRU 7.10.44R.
For interest rate risk, a VaR model must incorporate a set of risk factors corresponding to the interest rate curves in each currency in which the firm has interest rate sensitive positions. A firm must ensure that it captures the variations of volatility of rates along the yield curve. In order to achieve this, a firm must divide the yield curves of, at a minimum, the major currencies and markets in which it has material interest rate exposures into a minimum of six maturity segments. The VaR model must also capture the risk of less than perfectly correlated movements between different yield curves.
For foreign currency risk, a VaR model must incorporate risk factors corresponding to the individual foreign currencies, including gold, in which the firm's positions are denominated.
For commodity risk, the VaR model must use a separate risk factor at least for each commodity in which the firm has material positions. The VaR model must also capture the risk of less than perfectly correlated movements between similar, but not identical, commodities and the exposure to changes in forward prices arising from maturity mismatches. It must also take account of market characteristics, notably delivery dates and the scope provided to traders to close out positions.
- (1)
For CIUs the actual foreign currency positions of the CIU must be taken into account.
- (2)
A firm may rely on third party reporting of the foreign currency position of the CIU, where the correctness of this report is adequately ensured.
- (3)
If a firm is not aware of the foreign currency positions in a CIU, this position must be carved out and treated in BIPRU 7.5.18R (Derivation of notional positions in CIUs for the foreign currency PRR).
- (1)
This paragraph contains guidance on the inclusion of CIUs in a VaR model.
- (2)
The FSA may allow all types of CIU to be included within the scope of a firm's VaR model permission.
- (3)
BIPRU 7.10 does not distinguish between specific risk and general market risk for positions in CIUs. Therefore even if specific risk is not otherwise included within the scope of a firm's VaR model permission, a firm should be able to demonstrate that its VaR model captures specific risk.
- (4)
A firm should also be able to demonstrate that its VaR model adequately captures correlations, concentration risk and risks associated with the illiquidity of the CIU itself should this be deemed necessary (see BIPRU 7.10.32G).
- (5)
A firm may use a look-through approach, under which the VaR model estimates are based on the underlying positions. If a firm uses a look through approach it should also ensure that all the relevant risk factors relating to the underlying positions are captured. BIPRU 7.7 (Position risk requirements for collective investment undertakings) sets out rules relating to the look through approach when a firm is using the VaR model approach.
Model standards: Risk factors: Specific risk
- (1)
If a firm's VaR model covers the calculation of PRR with respect to specific risk the firm must meet the VaR specific risk minimum requirements in addition to the other requirements of BIPRU 7.10.
- (2)
The VaR model must explain the historical price variation in the portfolios concerned.
- (3)
The VaR model must capture concentration in terms of magnitude and changes of composition of the portfolios concerned.
- (4)
The VaR model must be robust to an adverse environment.
- (5)
The VaR model must capture name-related basis risk. That is the firm must be able to demonstrate that the VaR model is sensitive to material idiosyncratic differences between similar but not identical positions.
- (6)
The VaR model must capture event risk.
- (7)
In addition to the other requirements in BIPRU 7.10, a firm must have an approach in place to capture, in the calculation of its capital requirements, the default risk of its trading book positions that is incremental to the default risk captured by the VaR measures as specified in this rule, BIPRU 7.10.48R, BIPRU 7.10.49R and BIPRU 7.10.107R (Backtesting: Specific risk backtesting).
- (8)
A firm must be able to demonstrate that the approach referred to in (7) meets soundness standards comparable to the approach set out in BIPRU 4 (The IRB approach), under the assumption of a constant level of risk, and adjusted where appropriate to reflect the impact of liquidity, concentrations, hedging and optionality.
This paragraph provides guidance on BIPRU 7.10.46R (3). Take as an example a VaR model based on a factor model or on a historical simulation model. The ability of the model to explain price variation could be demonstrated by a statistical comparison over the same period of time between actual price changes on the portfolio and the profit and loss impact of risk factors included within the model. A firm may wish to include an estimate of residual variation not explained by the model.
- (1)
Where a firm is subject to event risk that is not reflected in its VaR measure, because it is beyond the 10-day holding period and 99 percent confidence interval (low probability and high severity events), the firm must ensure that the impact of such events is factored into its internal capital assessment.
- (2)
A firm's VaR model must conservatively assess the risk arising from less liquid positions and positions with limited price transparency under realistic market scenarios. In addition, the VaR model must meet minimum data standards. Proxies must be appropriately conservative and may be used only where available data is insufficient or is not reflective of the true volatility of a position or portfolio.
To avoid double counting capital requirements under BIPRU 7.10.46R (7) a firm may, when calculating its incremental default charge, take into account the extent to which default risk has already been incorporated into the VaR calculation, especially for risk positions that could and would be closed within 10 business days in the event of adverse market conditions or other indications of deterioration in the credit environment. Where a firm captures its incremental default risk through a surcharge, it must have in place methodologies for validating the measure.
A firm that does not capture the incremental default risk through an internally developed approach must calculate the surcharge through an approach consistent with either the standardised approach to credit risk or the IRB approach.
With respect to securitisation exposures that would be subject to a deduction treatment in the calculation of its capital resources or risk weighted at 1250% as set out in BIPRU 9, these positions (cash or synthetic) are subject to a capital charge that is no less than set forth under that treatment. A firm that is a dealer in these exposures may apply a different treatment where it could demonstrate to the FSA, in addition to trading intent, that a liquid two-way market exists for the securitisation exposures or, in the case of synthetic securitisation that rely solely on credit derivatives, for the securitisation exposures themselves or all their constituent risk components. For the purposes of this rule a two-way market is deemed to exist where there are independent good faith offers to buy and sell so that a price reasonably related to the last sales price or current good faith competitive bid and offer quotations can be determined within one day and settled at such a price within a relatively short time conforming to trade custom. For a firm to apply a different treatment, it must have sufficient market data to ensure that it fully captures the concentrated default risk of these exposures in its internal approach for measuring the incremental default risk in accordance with the VaR specific risk minimum requirements.
Model standards: Materiality
A firm's VaR model must capture accurately all material price risks for positions within the scope of its VaR permission, including risks relating to options or option-like positions. The firm must ensure that, if its VaR model does not accurately capture any material risk, the firm has capital resources adequate to cover that risk. These capital resources must be additional to those required to meet its capital resources requirement.
For example, BIPRU 7.10.53R might involve creating and documenting a prudent incremental PRR charge for the risk not captured in the VaR model and holding sufficient capital resources against this risk. In that case the firm should hold capital resources at least equal to its capital resources requirement as increased by adding this incremental charge to the model PRR. Alternatively the firm may make valuation adjustments through its profit and loss reserves to cover this material risk. These reserves should be transparent to senior management and auditable. The reserves should also be consistent with GENPRU 1.3 (Valuation) while not being excessive in relation to the principles of mark-to-market accounting. Therefore, a firm should be able to satisfy the FSA that all material risks are adequately addressed, whether this be through the VaR model, through taking an incremental PRR charge or through making an adjustment through profit and loss reserves.
A firm is expected ultimately to move towards full revaluation of option positions. For portfolios containing path dependent options, an instantaneous price shock applied to a static portfolio will be acceptable provided that the risks not captured by such an approach are not material. Where a risk is immaterial and does not justify further capital resources, that immaterial risk should still be documented.
Risk management standards: Introduction
A firm with a complex portfolio is expected to demonstrate greater sophistication in its modelling and risk management than a firm with a simple portfolio. For example, a firm will be expected to consider, where necessary, varying degrees of liquidity for different risk factors, the complexity of risk modelling across time zones, product categories and risk factors. Some trade-off is permissible between the sophistication and accuracy of the model and the conservatism of underlying assumptions or simplifications.
A firm should be able to demonstrate that it meets the risk management standards set out in the VaR model permission on a legal entity basis. This is particularly important for a subsidiary undertaking in a group subject to matrix management where the business lines cut across legal entity boundaries.
Risk management standards: General requirement
A firm must have a conceptually sound risk management system surrounding the use of its VaR model that is implemented with integrity and that in particular meet the qualitative standards set out in BIPRU 7.10.59R - BIPRU 7.10.82R.
Risk management standards: Use requirement
The VaR model must be fully integrated into the daily risk management process of the firm, and serve as the basis for reporting risk exposures to senior management of the firm.
A firm's VaR model output should be an integral part of the process of planning, monitoring and controlling a firm's market risk profile. The VaR model should be used in conjunction with internal trading and exposure limits. The links between these limits and the VaR model should be consistent over time and understood by senior management. The firm should regard risk control as an essential aspect of the business to which significant resources need to be devoted.
Risk management standards: Risk control unit
A firm must have a risk control unit which is independent from business trading units and which reports directly to senior management. It:
- (1)
must be responsible for designing and implementing the firm's risk management system;
- (2)
must produce and analyse daily reports on the output of the VaR model and on the appropriate measures to be taken in terms of the trading limits; and
- (3)
conduct the initial and on-going validation of the VaR model.
Risk management standards: Senior management
A firm's governing body and senior management must be actively involved in the risk control process, and the daily reports produced by the risk control unit must be reviewed by a level of management with sufficient authority to enforce both reductions of positions taken by individual traders as well as in the firm's overall risk exposure.
Risk management standards: Skilled staff
Risk management standards: Controls and compliance
A firm must establish, document and maintain policies, controls and procedures to an auditable standard:
- (1)
concerning the operation of its VaR model approach; and
- (2)
for monitoring and ensuring compliance with the policies, controls and procedures in (1).
Risk management standards: Documentation
- (1)
An example of documents required by BIPRU 7.10.67R may be a manual that describes the basic principles of the risk management framework, clearly setting out empirical techniques, principles and assumptions used within it.
- (2)
This documentation should be of sufficient detail for the FSA to be able to develop a clear understanding of how the VaR model works from that documentation on its own.
Risk management standards: Track record
Risk management standards: Development validation
Adequate procedures must be in place to ensure that model changes are validated before being introduced.
The procedures in BIPRU 7.10.70R need not necessarily rely on backtesting using a back-run of recreated data.
Risk management standards: Stress testing
- (1)
A firm must frequently conduct a rigorous programme of stress testing. The results of these tests must be reviewed by senior management and reflected in the policies and limits the firm sets.
- (2)
The programme must particularly address:
- (a)
concentration risk;
- (b)
illiquidity of markets in stressed market conditions;
- (c)
one way markets;
- (d)
event and jump to default risks;
- (e)
non linearity of products;
- (f)
deep out of the money positions;
- (g)
positions subject to the gapping of prices; and
- (h)
other risks that may not be captured appropriately in the VaR model (for example, recovery rate uncertainty, implied correlations and skew risk).
- (a)
- (3)
The shocks applied must reflect the nature of the portfolios and the time it could take to hedge out or manage risks under severe market conditions.
The stress testing under BIPRU 7.10.72R should be taken into account under the overall Pillar 2 rule.
Risk management standards: Valuation
Risk management standards: Risk review
At least once a year, a firm must conduct, as part of its regular internal audit process, a review of its risk management process. This review must include both the activities of the business trading units and of the independent risk control unit, and must be undertaken by suitably qualified staff independent of the areas being reviewed. This review must consider, at a minimum:
- (1)
the adequacy of the documentation of the risk management system and process;
- (2)
the organisation of the risk control unit;
- (3)
the integration of market risk measures into daily risk management;
- (4)
the integrity of the management information system;
- (5)
the process for approving risk pricing models and valuation systems used in front and back offices;
- (6)
the validation of any significant changes in the risk management process;
- (7)
the scope of risks and products captured by the VaR model;
- (8)
the accuracy and completeness of position data;
- (9)
the process used to ensure the consistency, timeliness, independence and reliability of data sources (including the independence of such data sources);
- (10)
the accuracy and appropriateness of volatility and correlation assumptions;
- (11)
reserving policies and the accuracy of the valuation procedures and risk sensitivity calculations;
- (12)
the process employed to evaluate the VaR model's accuracy, including the programme of backtesting;
- (13)
the controls surrounding the development of the VaR model; and
- (14)
the process employed to produce the calculation of the model PRR.
Risk management standards: Validation and backtesting
A firm must have processes in place to ensure that its VaR model has been adequately validated by suitably qualified parties independent of the development process to ensure that it is conceptually sound and adequately captures all material risks. This validation must be conducted when the VaR model is initially developed and when any significant changes are made to the VaR model. The validation must also be conducted on a periodic basis but especially where there have been any significant structural changes in the market or changes to the composition of the portfolio which might lead to the VaR model no longer being adequate. As techniques and best practices evolve, a firm must avail itself of these advances. Model validation must not be limited to backtesting, but must, at a minimum, also include the following:
- (1)
tests to demonstrate that any assumptions made within the VaR model are appropriate and do not underestimate or overestimate the risk (including testing of the validity of the assumptions and approximations underlying the VaR model);
- (2)
in addition to the regulatory backtesting programmes, a firm must carry out its own model validation tests in relation to the risks and structures of its portfolios, such as statistical validation techniques and other methods of measuring performance and validity;
- (3)
the use of hypothetical portfolios to ensure that the VaR model is able to account for particular structural features that may arise, for example material basis risks and concentration risk; and
- (4)
investigation of the limitations of the VaR model including testing of the accuracy of parts of the VaR model as well as of the whole.
- (1)
In addition to regulatory backtesting programs, testing for model validation should be carried out using additional tests which may include for example:
- (a)
testing carried out using hypothetical changes in portfolio value that would occur were end of day positions to remain unchanged;
- (b)
testing carried out for longer periods than required for the regular backtesting programme (for example, 3 years);
- (c)
testing carried out using confidence intervals other than the 99 percent interval required under the quantitative requirements in BIPRU 7.10; and
- (d)
testing of parts of portfolios.
- (a)
- (2)
A longer time period generally improves the power of backtesting. However a longer time period may not be desirable if the VaR model or market conditions have changed to the extent that historical data is no longer relevant.
Further material on backtesting can be found in BIPRU 7.10.91G - BIPRU 7.10.112G.
Risk management standards: Information technology
In assessing whether the VaR model is implemented with integrity as described in BIPRU 7.10.58R (Stress testing), the FSA will consider in particular the information technology systems used to run the model and associated calculations. The assessment may include:
- (1)
feeder systems; risk aggregation systems; time series databases; the VaR model system; stress testing system; the backtesting system including profit and loss cleaning systems where appropriate; data quality; reconciliations and checks on completeness of capture;
- (2)
system development, change control and documentation; security and audit trails; system availability and contingency procedures; network adequacy; and
- (3)
operational statistics relating to the VaR model production process, including, for example, statistics relating to timeliness, number of re-runs required and the reliability of data feeds.
Risk management standards: Controls
A firm must ensure that it has adequate controls relating to:
- (1)
the derivation of the model PRR;
- (2)
the integrity of the backtesting programme, including the calculation of the profit and loss account;
- (3)
the integrity and appropriateness of the VaR model, including the VaR model's geographic coverage and the completeness of data sources;
- (4)
the VaR model's initial and ongoing development, including independent validation;
- (5)
the valuation models, including independent validation; and
- (6)
the adequacy, security and integrity of the information technology infrastructure.
Stress testing
BIPRU 7.10.84G-BIPRU 7.10.90G relate to stress testing of a VaR model (see BIPRU 7.10.72R (Risk management standards: Stress testing)).
Stress testing is a way of identifying the risk to a firm posed by a breakdown of model assumptions or by low-probability events. Where stress tests reveal unacceptable vulnerability to a given set of circumstances, a firm should take prompt steps to manage those risks appropriately, for example by hedging against the outcome or reducing the size of the firm's exposure.
A firm must periodically and actively identify all the worst case scenarios that are relevant to its portfolio. Scenarios used must be appropriate to test the effect of adverse movements in market volatilities and correlations and the effect of any change in the assumptions underlying the VaR model. Scenarios involving low probability market events must nevertheless be plausible.
Stress testing must capture non-linear effects.
A firm must have procedures to assess and respond to the results produced from stress testing. In particular, stress testing results must be:
- (1)
used to evaluate its capacity to absorb such losses or identify steps to be taken to reduce risk; and
- (2)
communicated routinely to senior management and periodically to the governing body.
Backtesting: Introduction
Backtesting is the process of comparing value-at-risk risk measures to portfolio performance. It is intended to act as one of the mechanisms for the ongoing validation of a firm's VaR model and to provide incentives for firms to improve their VaR measures.
It is a condition for granting a VaR model permission that a firm should have a backtesting programme in place and should provide three months of backtesting history.
Backtesting conducted only at a whole portfolio level using a single measure of profit and loss has limited power to distinguish an accurate VaR model from an inaccurate one. Backtesting should therefore be regarded as an additional safeguard rather than a primary validation tool. Such testing does however form the basis of the FSA's plus factor system. The test has been chosen as the basis of the backtesting regime because of its simplicity. A firm will therefore be expected to complement this backtesting with more granular backtesting analysis and involving more than one measure of profit and loss (i.e. both a clean profit and loss figure and a clean hypothetical profit and loss figure).
A firm must have the capacity to analyse and compare its clean profit and loss figures and clean hypothetical profit and loss figures to the VaR measure, both at the level of the whole portfolio covered by the VaR model permission and at the level of individual books that contain material amounts of risk.
Clean profit and loss backtesting should be used for regulatory backtesting and used to calculate plus factors. Hypothetical profit and loss backtesting is used for model validation and for reporting to the FSA.
Backtesting: Basic testing requirements
A firm must, on each business day, compare each of its 250 most recent business days' clean profit and loss figures (ending with the business day preceding the business day in question) with the corresponding one-day VaR measures.
Generally the positions underlying the profit and loss account and VaR measures should not be materially different.
Backtesting: One day VaR measure
The one-day VaR measure for a particular business day is the VaR number for that business day calibrated to a one business day holding period and a 99% one-tailed confidence level.
Backtesting: Calculating the clean profit and loss
The ultimate purpose of backtesting is to assess whether capital is sufficient to absorb actual losses. Therefore backtesting should be performed using a measure of actual daily profit and loss. Actual daily profit and loss means the day's profit and loss arising from trading activities within the scope of the VaR model permission. This measure should, however, be 'cleaned' using BIPRU 7.10.100R inclusion in profit and loss of non-modelled factors.
The clean profit and loss figure for a particular business day is the firm's actual profit or loss for that day in respect of the trading activities within the scope of the firm's VaR model permission, adjusted by stripping out:
- (1)
fees and commissions;
- (2)
brokerage;
- (3)
additions to and releases from reserves which are not directly related to market risk (e.g. administration reserves); and
- (4)
any inception profit exceeding an amount specified for this purpose in the firm's VaR model permission (where inception profit is defined as any profit arising immediately on entering into a new transaction).
The definition of clean profit and loss figure may be amended or replaced in an individual VaR model permission if the firm can demonstrate to the FSA that the alternative method meets the spirit and purpose of the provisions in BIPRU 7.10 about the clean profit and loss figure.
The FSA will review as part of a firm's VaR model permission application the processes and documentation relating to the derivation of profit and loss used for backtesting. A firm's documentation should clearly set out the basis for cleaning profit and loss. To the extent that certain profit and loss elements are not updated every day (for example certain reserve calculations) the documentation should clearly set out how such elements are included in the clean profit and loss series.
Backtesting: Definition of backtesting exception
A backtesting exception is deemed to have occurred for any business day if the clean profit and loss figure for that business day shows a loss, which in absolute magnitude, exceeds the one-day VaR measure for that business day. The only exception is if that business day is identified in the firm's VaR model permission as giving rise to an excluded backtesting exception.
Backtesting: Obligation to notify the FSA
If a backtesting exception occurs, the firm must notify its usual supervisory contact at the FSA orally by close of business two business days after the business day for which the backtesting exception occurred. Within five business days following the end of each Month, the firm must submit to the FSA a written account of the previous Month's backtesting exceptions (if any). This explanation must include the causes of the backtesting exceptions, an analysis of whether the backtesting exception indicate a deficiency in the firm's VaR model and the firm's planned response (if any).
Backtesting: Summary of the backtesting cycle
- (1)
This paragraph gives guidance on the backtesting calculation and reporting process in BIPRU 7.10.96R - BIPRU 7.10.104R.
- (2)
Let the day on which the loss referred to in BIPRU 7.10.100R is made be day n. The value-at-risk measure for that day will be calculated on day n-1, or overnight between day n-1 and day n. Profit and loss figures are produced on day n+1, and backtesting also takes place on day n+1. The firm's supervisor should be notified of any backtesting exceptions by close of business on day n+2.
- (3)
Any backtesting exception initially counts for the purpose of the calculation of the plus factor even if subsequently the FSA agrees to exclude it under the process described in BIPRU 7.10.106G. Thus, where the firm experiences a backtesting exception and already has four or more backtesting exceptions for the previous 250 business days, changes to the multiplication factor arising from changes to the plus factor become effective at n+3 (using the time-line terminology in (2)).
Backtesting: Process for disregarding backtesting exceptions
- (1)
This paragraph gives guidance on the process for excluding backtesting exceptions as referred to in BIPRU 7.10.103R.
- (2)
The FSA will respond flexibly to backtesting exceptions. However, the FSA's starting assumption will be that a backtesting exception should be taken into account for the purpose of the calculation of plus factors. If the firm believes that a backtesting exception should not count for that purpose, then it should seek a variation of its VaR model permission in order to exclude that particular backtesting exception. The FSA will then decide whether to agree to such a variation.
- (3)
One example of when a firm's backtesting exception might properly be disregarded is when it has arisen as a result of a risk that is not captured in its VaR model but against which capital resources are already held.
Backtesting: Specific risk backtesting
If a firm's VaR model permission covers specific risk, the firm must validate its VaR model through backtesting aimed at assessing whether specific risk is being accurately captured. This backtesting must be carried out in accordance with the provisions of its VaR model permission. If the VaR model permission provides for this backtesting to be performed on the basis of relevant sub-portfolios, these must be chosen in a consistent manner.
Specific risk backtesting involves the backtesting of a standalone specific risk VaR measure against a profit and loss series determined by reference to exposure risk factors categorised as specific risk. Alternatively specific risk backtesting may take the form of regular backtesting of trading books and portfolios that are predominantly exposed to risk factors categorised as specific risk. The precise requirements for specific risk backtesting will be specified in the firm's VaR model permission as will the definition of a specific risk backtesting exception.
Backtesting: Multiple exceptions
If ten or more backtesting exceptions or ten or more specific risk backtesting exceptions are recorded in a 250 business day period, a firm must take immediate corrective action.
Where backtesting reveals severe problems with the basic integrity of the VaR model, the FSA may withdraw model recognition. In particular, if ten or more backtesting exceptions are recorded in a 250 business day period, the FSA may apply a plus factor greater than one or the FSA may consider revoking a firm's VaR model permission. The FSA may also consider revoking a firm's VaR model permission if ten or more specific risk backtesting exceptions occur in such a period.
Backtesting: Hypothetical profit and loss
A firm must also perform backtesting against a clean hypothetical profit and loss figure with respect to each business day. A clean hypothetical profit and loss figure for a business day means the clean profit and loss figure that would have occurred for that business day if the portfolio on which the VaR number for that business day is based remained unchanged.
- (1)
A clean hypothetical profit and loss figure is based on the day's change in the value of the same portfolio that was used to generate the value-at-risk forecast.
- (2)
Backtesting under BIPRU 7.10.111R, although carried out with respect to each business day, need not be carried out each day. A firm need only carry it out sufficiently frequently to comply with its reporting requirements under BIPRU 7.10.129R. An exception arising out of such backtesting need not be reported to the FSA under BIPRU 7.10.104R
- (3)
The firm may also need to calculate a clean hypothetical profit and loss figure in order to produce profit attribution reports and to analyse the cause of backtesting exceptions.
Capital calculations: General
The model PRR is, for any business day (the "relevant" business day), calculated in accordance with the following formula:
- (1)
the higher of:
- (a)
the VaR number for the relevant business day; and
- (b)
the average of its daily VaR numbers for each of the 60 business days ending with the relevant business day, multiplied by the multiplication factor for the relevant business day; and
- (a)
- (2)
(in the case of a VaR model permission that covers specific risk) the incremental default risk charge for the relevant business day.
For any day that is not a business day, the model PRR is the amount for the prior business day.
The VaR number for any business day means the VaR measure, in respect of the previous business day's close-of-business positions in products coming within the scope of the VaR model permission, calculated by the VaR model and in accordance with BIPRU 7.10 and any methodology set out in the VaR model permission. The VaR number must not be calculated taking into account matters on the business day for which it is the VaR number.
The incremental default risk charge for any business day means the incremental default risk charge required under the provisions in BIPRU 7.10 about specific risk, in respect of the previous business day's close-of-business positions with respect to which those provisions apply.
The following equation expresses BIPRU 7.10.113R mathematically:
where:
- (1)
- (2)
VaR t represents the previous day's value-at-risk figure;
- (3)
VaR t-i represents the value-at-risk calculated for i business days earlier;
- (4)
f is the multiplication factor; and
- (5)
IDRC is the incremental default risk charge (if applicable).
Capital calculations: Multiplication factors
The multiplication factor for any business day is the sum of the minimum multiplication factor and the plus factor for that day.
The minimum multiplication factor is three or any higher amount the VaR model permission defines it as.
The minimum multiplication factor will never be less than three. If the FSA does set the minimum multiplication factor above three the VaR model permission will have a table that sets outs the reasons for that add on and specify how much of the add on is attributable to each reason (see BIPRU 7.10.121R). If there are weaknesses in the VaR model that may otherwise be considered a breach of the minimum standards referred to in BIPRU 7.10.24R the FSA may apply such an add on to act as a mitigant for those weaknesses.
Something that would otherwise be a breach of the minimum standards to in BIPRU 7.10.26R - BIPRU 7.10.53R is not a breach to the extent that that thing is identified in the firm's VaR permission as a reason for an increase in the minimum multiplication factor above 3.
Typically, any add on will be due to a specific weakness in systems and controls identified during the FSA's review that the FSA does not consider material enough to justify withholding overall model recognition. The firm will be expected to take action to address the reasons for any add on. The FSA will then review these periodically and, where satisfactory action has been taken, the add on will be removed through a variation of the VaR model permission.
The plus factor system is designed so that the more often a VaR model has under-predicted losses in the past, the higher should be the capital requirement based on the VaR model. It is intended to provide a capital incentive for the firm to continue to improve the accuracy of its VaR model.
The table in BIPRU 7.10.125R sets out the plus factors to be added to the minimum multiplication factor for any business day. It is based on the number of backtesting exceptions that occurred during the backtesting period as referred to in BIPRU 7.10.96R (Backtesting: Basic testing requirements) ending three business days preceding the business day for which the model PRR is being calculated.
Table: Backtesting plus factors
This table belongs to BIPRU 7.10.124R
Zone |
Number of recorded exceptions |
Plus factor |
Green |
4 or less |
0.00 |
Yellow |
5 |
0.40 |
6 |
0.50 |
|
7 |
0.65 |
|
8 |
0.75 |
|
9 |
0.85 |
|
Red |
10 or more |
1.00 |
A VaR model that correctly predicts a one-tailed 99% confidence level is expected to produce, on average, 2.5 backtesting exceptions every 250 days. Random events may cause the number of backtesting exceptions actually observed to vary. The plus factor system is designed to take this into account. Hence plus factors are only imposed on the firm if it has five or more recorded backtesting exceptions. Therefore, where a backtesting exception appears to be caused simply by chance, it will not be appropriate for a VaR model permission to be varied to exclude that backtesting exception as described in BIPRU 7.10.106G (Backtesting: Process for disregarding backtesting exceptions).
Capital calculations: Specific risk surcharge: transitional requirements
Firms who gained model recognition before 1 January 2007 will be permitted to calculate PRR for specific risk in accordance with the methodology they were permitted to use immediately before that date instead of capturing event and default risk in their models (see BIPRU TP 14 (Market risk: VaR models)). This treatment will not be available to a firm that gains model recognition after that date.
Reporting procedures and requirements
A VaR model permission will contain requirements for what the firm should report to the FSA and the procedures for reporting. The precise requirements will vary from VaR model permission to VaR model permission. BIPRU 7.10.129R-BIPRU 7.10.130R set out what the FSA regards as the standard requirements.
A firm must, no later than the number of business days after the end of each quarter specified in the VaR model permission for this purpose, submit, in respect of that quarter, a report to the FSA about the operation of the VaR model, the systems and controls relating to it and any changes to the VaR model and those systems and controls. Each report must outline as a minimum the following information in respect of that quarter:
- (1)
methodological changes and developments to the VaR model;
- (2)
the introduction of all new pricing models used in connection with the VaR model and any changes to any pricing models used in connection with the VaR model, including details of any material associated valuation or risk management issues;
- (3)
a summary of backtesting performance against clean profit and loss figures and clean hypothetical profit and loss figures, which must be provided in electronic format as stipulated by the VaR model permission;
- (4)
(if the VaR model permission covers specific risk) the results of the specific risk backtesting including specific risk backtesting exceptions;
- (5)
any change to any feeder or pre-processing systems in connection with the VaR model, including changes to any of the systems set out in the list described in BIPRU 7.10.131G (1) (as it exists at the date of the VaR model permission), and any introduction of a new such system;
- (6)
any changes to the products coming within the scope of the VaR model;
- (7)
any material changes or additions to any of the matters referred to in the firm's internal documentation in relation to the VaR model (as it exists at the date of the VaR model permission) or to any matters subsequently notified under (7);
- (8)
any changes in senior management;
- (9)
an up-to-date list of products covered by the VaR model permission showing all changes made since the VaR model permission was granted; and
- (10)
where applicable (nil returns are not required), details of:
- (a)
any use of a changed historical observation period in accordance with BIPRU 7.10.30R or any change in the use of any weighting scheme as described in BIPRU 7.10.33R;
- (b)
any data series becoming unreliable as described in BIPRU 7.10.31R and any subsequent use of alternative value-at-risk measurement techniques;
- (c)
the frequency of updating data sets being increased in accordance with BIPRU 7.10.34R;
- (d)
any change in the method employed to derive 10-day VaR measure (see BIPRU 7.10.28R);
- (e)
to the extent that the use of correlations is permitted by a firm's VaR model permission, a summary of any notifications that are required under BIPRU 7.10.37R; and
- (f)
the VaR model not accurately capturing risks (as referred to in BIPRU 7.10.53R) and any steps taken under BIPRU 7.10.53R.
- (a)
A firm must provide to, and discuss with, the FSA details of any significant planned changes to the VaR model before those changes are implemented. These details must include information about the nature of the change and an estimate of the impact on VaR numbers and the incremental default risk charge.
Updating the VaR model permission
The VaR model permission will generally contain a list of the following:
- (1)
feeder systems and pre-processing systems;
- (2)
products covered by the VaR model permission; and
- (3)
the firm's internal documentation in relation to the VaR model.
The information in BIPRU 7.10.131G will vary over time. It is therefore not included in a VaR model permission as a rule but for information only. The FSA will update that information regularly in accordance with information supplied under BIPRU 7.10.129R. That updating will not amount to a variation of the VaR model permission.
Link to standard PRR rules: Incorporation of the model output into the capital calculation
A VaR model permission will modify GENPRU 2.1.52 R (Calculation of the market risk capital requirement) to provide that a firm should calculate its market risk capital requirement in accordance with BIPRU 7.10 to the extent set out in the VaR model permission.
By modifying GENPRU 2.1.52 R (Calculation of the market risk capital requirement) to allow the firm to use the VaR model to calculate all or part of its PRR for certain positions, the FSA is treating it like an application rule. The modification means that the PRR calculation set out in BIPRU 7.10 supersedes the standard market risk PRR rules for products and risks coming within the scope of the VaR model permission.
- (1)
This rule applies to a position of a type that comes within the scope of a firm's VaR model permission.
- (2)
If, where the standard market risk PRR rules apply, a position is subject to a PRR charge and the firm's VaR model permission says that it covers the risks to which that PRR charge relates, the firm must, for those risks, calculate the PRR for that position under the VaR model approach rather than under the standard market risk PRR rules.
- (3)
If, where the standard market risk PRR rules apply, a position is subject to one or more PRR charges and the firm's VaR model permission does not cover all the risks to which those PRR charges relate, the firm must calculate the PRR for that position under the VaR model approach (for those risks that are covered) and under the standard market risk PRR rules (for those other risks).
- (4)
Where the standard market risk PRR rules distinguish between specific risk and general market risk a firm's VaR model permission covers specific risk to the extent that it says it does. If the firm's VaR model permission does not cover specific risk, BIPRU 7.10.143R and BIPRU 7.10.144R apply.
- (5)
If a firm's VaR model permission covers positions in CIUs it covers specific risk with respect to those positions.
A firm may exclude from the VaR model approach immaterial risks within the scope of its VaR model approach. If a firm does so it must instead apply the standard market risk PRR rules to those risks.
- (1)
If a firm calculates its market risk capital requirement using a combination of the standard market risk PRR rules and either the VaR model approach or the VaR model approach with the CAD 1 model approach the PRR from each method must be added together.
- (2)
A firm must take appropriate steps to ensure that all of the approaches are applied in a consistent manner.
An example of the effect of BIPRU 7.10.138R is that where a firm normally calculates the PRR for a particular portfolio using a VaR model, a firm should not switch to the standard market risk PRR rules purely to achieve a more attractive PRR.
If:
- (1)
the standard market risk PRR rules provide for a choice of which of the PRR charges to use or specify that one type must be used in some circumstances and that another type must be used in other circumstances;
- (2)
one of those types is disapplied under BIPRU 7.10.136R; and
- (3)
the other type is not disapplied;
the firm:
- (4)
must use the VaR model approach if under the standard market risk PRR rules the firm must use the standard market risk PRR rules in (2); and
- (5)
may use the VaR model approach if under the standard market risk PRR rules the firm may use the standard market risk PRR rules in (2).
The treatment of a convertible is an example of a situation in which BIPRU 7.10.140R applies. The table in BIPRU 7.3.3R (Table: Instruments which result in notional positions) shows that there are circumstances in which under the standard market risk PRR rules a firm should calculate an equity PRR and that there are circumstances in which a firm may choose between calculating an equity PRR and an interest rate PRR. BIPRU 7.10.140R would be relevant if a firm's VaR model permission only covers one of equity risk and interest rate risk.
The standard market risk PRR rules for the option PRR are only disapplied to the extent that the derived positions arising under BIPRU 7.6.13R (Table: Derived positions) come within the scope of the VaR model permission.
Link to standard PRR rules: General market risk only
If a firm's VaR model permission covers interest rate general market risk but not interest rate specific risk, the firm must calculate the interest rate PRR so far as it relates to interest rate specific risk in accordance with the standard market risk PRR rules except that the firm must not use the basic interest rate PRR calculation in BIPRU 7.3.45R (Basic interest rate calculation for equity instruments).
Link to standard PRR rules: General market risk only
If a firm's VaR model permission covers equity general market risk but not equity specific risk, the firm must calculate the equity PRR so far as it relates to equity specific risk in accordance with the standard market risk PRR rules except that the PRR for equity specific risk must be calculated under the standard equity method.
Link to standard PRR rules: Miscellaneous
- (1)
To the extent that a firm's VaR model permission does not allow it to use an approach set out in BIPRU 7.10 the relevant provisions in BIPRU 7.10 do not apply to that firm.
- (2)
If a provision of the Handbook refers to BIPRU 7.10, that reference must, in the case of a particular firm with a VaR model permission, be treated as excluding provisions of BIPRU 7.10 that do not apply under the VaR model permission and as taking into account any modifications to BIPRU 7.10 made by the VaR model permission. Such references also include requirements and conditions contained in the VaR model permission but not BIPRU 7.10 and to the rules modified by the VaR model permission.
Requirement to use value at risk methodology
Ceasing to meet the requirements of BIPRU 7.10
If a firm ceases to meet any of the requirements set out in BIPRU 7.10, the FSA's policy is that the VaR model permission should cease to have effect. In part this will be achieved by making it a condition of a firm's VaR model permission that it complies at all times with the minimum standards referred to in BIPRU 7.10.26R - BIPRU 7.10.53R. Even if they are not formally included as conditions, the FSA is likely to consider revoking the VaR model permission if the requirements are not met.
If a firm ceases to meet the conditions or requirements in its VaR model permission or BIPRU 7.10 it must notify the FSA at once.
Changes to a VaR model
A firm may change its VaR model to such extent as it sees fit, except that it must not make a change that (either on its own or together with other changes since the date of VaR model permission) would:
- (1)
be inconsistent with VaR model permission or BIPRU 7.10; or
- (2)
mean that backtesting in accordance with BIPRU 7.10 and the VaR model permission would result in the use of data that is inappropriate for the purposes of measuring the performance of the VaR model.