D. Use of Internal Models
11. This section sets out the conditions under which a Bank is permitted to use an internal model to calculate its Market Risk Capital Requirement or any component of its Market Risk Capital Requirement. A Bank that wishes to use an internal model to calculate any part of this requirement is required to apply to the AFSA. Internal models will commonly permit more extensive netting of long and short positions and have greater risk sensitivity.
12. In assessing whether to give approval, the AFSA will consider the effectiveness and coverage of the Bank’s risk management framework, governance of its model development and implementation processes, the stress-testing and back-testing standards and the process surrounding the calculation of capital requirements.
13. The AFSA will usually approve the use of an internal model if:
(a) the use of the model to calculate the Market Risk Capital Requirement has been approved by another appropriate regulator or the Bank has provided opinions from independent experts on the ability of the model to calculate Market Risk capital requirements, to the satisfaction of the AFSA;
(b) use of the methodology is integrated into the governance and risk management framework of the Bank. Specifically, the Governing Body and senior management of the Bank receives and reviews appropriate reports in respect of the model and its use;
(c) it is satisfied with the overall soundness and integrity of the Bank's enterprise-wide risk management system;
(d) the Bank has sufficient numbers of staff skilled in the use of sophisticated models specifically in the risk management, audit, and back office areas;
(e) the Bank's models have a proven track record of reasonable accuracy in measuring risk; and
(f) the Bank has a robust stress testing programme.
14. In determining whether an internal value at risk (VaR) model meets the standard for approval, the AFSA will apply the criteria set out in the section below, which are based on the Basel Market Risk Capital Amendment 1996 and Basel Revisions to the Basel II Market Risk framework 2009 and which can be grouped under the following headings:
(a) qualitative standards;
(b) specification of Market Risk factors;
(c) quantitative standards;
(d) adjustments to Market Risk Capital Requirements;
(e) stress testing; and
(f) combination of internally developed models and the Standardised Methodology.
15. In addition to VaR models, the AFSA is open to considering the use of option risk aggregation models and interest rate ‘pre-processing’ or sensitivity models, Option risk aggregation models analyse and aggregate options risks for interest rate, equity, foreign exchange and commodity options. Interest rate pre-processing models are used to calculate weighted positions for inclusion in a Bank’s interest rate Market Risk Capital Requirement calculation under the Duration Method.
16. Any internal model used for purposes of Chapter 6 of BBR should be conceptually sound and implemented with integrity and, in particular, all of the following qualitative requirements should be met:
(a) any internal model used to calculate Market Risk Capital Requirements for equity risk, interest rate risk, foreign exchange risk or commodities risk should be closely integrated into the daily risk management process and serve as the basis for reporting risk Exposures to senior management;
(b) the Bank should have a risk control unit that is independent from business trading units and reports directly to senior management. The unit should be responsible for designing and implementing any internal model used for purposes of Chapter 6 of BBR. The unit should conduct the initial and on-going validation of any such internal models. The unit should produce and analyse daily reports on the output of any internal model used for calculating Capital Requirements for position risk, foreign exchange risk and commodities risk, and on the appropriate measures to be taken in terms of trading limits;
(c) the Bank's Governing body and senior management should be actively involved in the risk control process and the daily reports produced by the risk control unit are reviewed by a level of management with sufficient authority to enforce both reductions of positions taken by individual traders as well as in the Bank's overall risk Exposure;
(d) the Bank should have established procedures for monitoring and ensuring compliance with a documented set of internal policies and controls concerning the overall operation of its internal models;
(e) the Bank should frequently conduct a rigorous programme of stress testing, including reverse stress tests, which encompasses any internal model used for purposes of Chapter 6 of BBR and the results of these stress tests should be reviewed by senior management and reflected in the policies and limits it sets. This process should particularly address illiquidity of markets in stressed market conditions, concentration, one way markets, event and jump-to-default risks, non-linearity of products, deep out-of-the-money positions, positions subject to the gapping of prices and other risks that may not be captured appropriately in the internal models. The shocks applied should reflect the nature of the portfolios and the time it could take to hedge out or manage risks under severe market conditions; and
(f) the Bank should conduct, as part of its regular internal auditing process, an independent review of its internal models.
17. The independent review of the internal models used by a Bank, must include the activities of both the business trading units and of the independent risk-control unit. At least once a year, the Bank should conduct a review of its overall risk management process. The review should consider the following:
(a) the adequacy of the documentation of the risk-management system and process and the organisation of the risk-control unit;
(b) the integration of risk measures into daily risk management and the integrity of the management information system;
(c) the process the Bank employs for approving risk-pricing models and valuation systems that are used by front and back-office personnel;
(d) the scope of risks captured by the risk-measurement model and the validation of any significant changes in the risk-measurement process;
(e) the accuracy and completeness of position data, the appropriateness of volatility and correlation assumptions, and the accuracy of valuation and risk sensitivity calculations;
(f) the verification process used to evaluate the consistency, timeliness and reliability of data sources used to run internal models, including the independence of such data sources; and
(g) the verification process used to evaluate back-testing for the internal models' accuracy.
18. As techniques and best practices evolve, Banks are expected to apply those new techniques and practices in any internal model used for purposes of Chapter 6 of BBR.
19. Any internal model used to calculate Capital Requirements for equity position risk, interest rate risk, foreign exchange risk, commodities risk and any internal model for correlation trading should meet all of the following requirements:
(a) the model must capture accurately reflect, on a continuous basis, all material price risks, including General Market Risks and, where approval has been granted in relation to specific Risk, specific risks arising on the underlying portfolio, and should ensure that sufficient risk factors are properly specified; and
(b) the model should capture a sufficient number of risk factors, depending on the level of activity of the Bank in the respective markets. The risk factors in the model should be sufficient to capture the risks inherent in the Bank’s portfolio of on and off-balance sheet trading positions. The Bank should at least incorporate those risk factors in its model that are incorporated into its pricing model.
(c) The risk-measurement model should capture nonlinearities for options and other products as well as correlation risk and basis risk. Where proxies for risk factors are used they should show a good track record for the actual position held. Although a Bank will have some discretion in specifying the risk factors for its internal models, the AFSA expects that such models will meet the criteria specified in this guideline.
20. Any internal model used to calculate Capital Requirements for position risk, foreign exchange risk or commodities risk should meet all of the following requirements:
(a) the model should incorporate a set of risk factors corresponding to the interest rates in each currency in which the Bank has interest rate sensitive on or off balance sheet positions. The Bank should model the yield curves using one of a number of generally accepted approaches, for example, by estimating forward rates of zero-coupon yields;
(b) for material Exposures to interest-rate risk in the major currencies and markets, the yield curve should be divided into a minimum of six maturity segments, to capture the variations of volatility of rates along the yield curve. The model should also capture the risk of less than perfectly correlated movements between different yield curves. The risk measurement system should incorporate separate risk factors to capture spread risk, for example, between bonds and swaps;
(c) the model should incorporate risk factors corresponding to gold and to the individual foreign currencies in which the Bank's positions are denominated.
(d) for Collective Investment Funds the actual foreign exchange positions of the Fund should be taken into account. Banks may rely on third party reporting of the foreign exchange position of the Fund, where the correctness of this report is adequately ensured. If a Bank is not aware of the foreign exchange positions of a Fund, this position should be carved out of the model and treated separately;
(e) the model should use a separate risk factor at least for each of the equity markets in which the Bank holds significant positions. At a minimum, this will include a risk factor that is designed to capture market-wide movements in equity prices, for example, a market index. Positions in individual securities or in sector indices could be expressed in “beta-equivalents” relative to this market-wide index. A relatively more- detailed approach would be to have risk factors corresponding to various sectors of the overall equity market, for instance, industry sectors or cyclical and non-cyclical sectors. The most extensive approach would be to have risk factors corresponding to the volatility of individual equity issues;
(f) the model should use a separate risk factor at least for each commodity in which the Bank holds significant positions. The 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 should also take account of market characteristics, notably delivery dates and the scope provided to traders to close out positions; For more actively traded portfolios, the model should also take account of variation in the “convenience yield” between derivative positions such as forwards and swaps and cash positions in the commodity; and
(g) the Bank's internal model should conservatively assess the risk arising from less liquid positions and positions with limited price transparency under realistic market scenarios. In addition, the internal model should meet minimum data standards. Proxies should be appropriately conservative and should be used only where available data is insufficient or is not reflective of the true volatility of a position or portfolio.
21. Banks may use empirical correlations within risk categories and across risk categories only if the Bank's approach for measuring correlations is sound and implemented with integrity.
22. The AFSA will usually approve an internal Value-at-Risk (VaR) model, for the purposes of Chapter 6 of the BBR only when that VaR model meets the following quantitative criteria:
(a) VaR should be computed at least on a daily basis;
(b) in calculating the value-at-risk, a 99th percentile, one-tailed confidence interval is to be used;
(c) in calculating VaR, an instantaneous price shock equivalent to a 10 day movement in prices is to be used, i.e., the minimum "holding period" will be 10 trading days;
(d) an effective historical observation period of at least one year except where a shorter observation period is justified by a significant upsurge in price volatility; and
(e) its data set is updated by the Bank no less frequently than once every month and is reassessed whenever market prices are subject to material changes.
23. A bank may use VaR numbers calculated according to shorter holding periods than 10 days scaled up to 10 days by an appropriate methodology.
24. The AFSA prescribes no particular type of model so long as the model used captures all the material exposures of the Bank. The Bank will be free to use models based, for example, on variance- covariance matrices, historical simulations, or Monte Carlo simulations. Banks have discretion to recognise empirical correlations within broad risk categories, for example, interest rates, exchange rates, equity prices and commodity prices, including related options volatilities in each risk factor category.
25. A Bank's internal models should accurately capture the unique risks associated with options within each of the broad risk categories. A Bank should calculate, on a daily basis, its Market Risk Capital Requirement or any component for which an internal model is used, expressed as the higher of (a)
its previous day's VaR number measured according to the parameters specified in this section and
(b) an average of the daily VaR measures on each of the preceding sixty business days, multiplied by a multiplication factor.
26. The AFSA will usually set a multiplication factor of 3 that must be used by the Bank where all the qualitative and quantitative criteria are satisfied. This will be imposed as a condition on the approval and may be varied by the AFSA should circumstances require.
27. A Bank using internal VaR models is expected to calculate a ‘Stressed VaR' of the current portfolio, at least on a weekly basis, in addition to the calculation of VaR in accordance with the requirements set out in this section. The VaR model inputs for calculation of Stressed VaR should ideally be calibrated to historical data from a continuous 12-month period of significant financial stress relevant to the Bank's portfolio. The choice of such historical data should be subject to review by the Bank, at least on an annual basis and the outcome of such a review must be notified to the AFSA promptly.
28. A Bank using an internal model should calculate Capital Requirement for the relevant risk categories, as the sum of points (a) and (b):
(a) the higher of:
i) its previous day's VaR number calculated in accordance with the guidance in this section; or
ii) an average of the daily VaR numbers calculated in accordance with the guidance in this section, on each of the preceding sixty business days (AvgVaR), multiplied by the multiplication factor referred in paragraph 26 above; plus
(b) the higher of:
i) its latest available stressed VaR number calculated in accordance with guidance in this section (sVaRt-1); or
ii) an average of the stressed VaR numbers calculated in accordance with the guidance in this section, over the preceding sixty business days (Avg sVaR), multiplied by the multiplication factor referred in Guidance note 16 above.
Regulatory back-testing and multiplication factors
29. The results of the Stressed VaR calculations referred in this section must be scaled up by the multiplication factors given below. The multiplication factor referred above is defined as the sum of 3 and an addend between 0 and 1. That addend should depend on the number of violations for the most recent 250 business days as evidenced by the Bank’s back-testing of the VaR as set out in the guidance in this section.
Number of violations | addend |
Fewer than 5 | 0.00 |
5 | 0.40 |
6 | 0.50 |
7 | 0.65 |
8 | 0.75 |
9 | 0.85 |
10 or more | 1.00 |
For example, if the number of violations (as defined in the following paragraph) observed on the back- testing results of a Bank over the most recent 250 business days is 6, then the multiplication factor to scale the Stressed VaR result would be 3.5. This is determined by adding 3 with the addend from the table for 6 violations, which is 0.5. So, if the calculated stressed VaR for the Bank is USD 300 million, then it must be scaled up to a stressed VaR of USD 1050 million (3.5*300 million). This clearly points to the penalizing impact of the scaling factor for models which perform poorly in back testing. The minimum scaling factor is 3, even if the number of violations observed over the most recent 250 business days happens to be 0.
… Please provide an example of application the above table.
30. A Bank should count daily violations on the basis of back-testing on hypothetical and actual changes in the portfolio's value. A violation for this purpose is defined as a one-day change in the portfolio's value that exceeds the related one-day VaR number generated by the Bank's model. For the purpose of determining the addend the number of violations should be assessed at least on a quarterly basis and should be equal to the higher of the number of violations under hypothetical and actual changes in the value of the portfolio.
31. Back-testing on hypothetical changes in the portfolio's value should be based on a comparison between the portfolio's end-of-day value and, assuming unchanged positions, its value at the end of the subsequent day. Back-testing on actual changes in the portfolio's value should be based on a comparison between the portfolio's end-of-day value and its actual value at the end of the subsequent day excluding fees, commissions, and net interest income.
32. The AFSA may in individual cases limit the addend to that resulting from violations under hypothetical changes, where the number of violations under actual changes does not result from deficiencies in the internal model. In order to enable the AFSA to monitor the appropriateness of the multiplication factors on an ongoing basis, the Bank should notify any violations that result from its back-testing programme promptly, and in any case no later than five working days from the date of its identification.
33. Banks should have processes in place to ensure that all their internal models have been adequately validated by suitably qualified parties independent of the development process to ensure that they are sound and adequately capture all material risks. The validation should be conducted when the internal model is initially developed and when any significant changes are made to the internal model.
34. The validation should also be conducted on a periodic basis, especially where there have been significant structural changes in the market or changes to the composition of the portfolio which might result in the internal model being no longer adequate. As techniques and best practices for internal validation evolve, Banks are expected to apply such improvements. Internal model validation should not be limited to back-testing, but should, at a minimum, also include the following:
(a) tests to demonstrate that any assumptions made within the internal model are appropriate and do not underestimate or overestimate the risk;
(b) Banks should carry out their own internal model validation tests, including back-testing, in relation to the risks and structures of their portfolios; and
(c) the use of hypothetical portfolios to ensure that the internal model is able to account for particular structural features that may arise, for example material basis risks and concentration.
35. The Bank should perform back-testing on both actual and hypothetical changes in the portfolio's value. An internal model used for calculating Capital Requirements for specific risk and an internal model for correlation trading should meet the following additional requirements:
(a) it explains the historical price variation in the portfolio;
(b) it captures concentration in terms of magnitude and changes of composition of the portfolio;
(c) it is robust to an adverse environment;
(d) it is validated through back-testing aimed at assessing whether specific risk is being accurately captured. If the Bank performs such back-testing on the basis of relevant sub- portfolios, these must be chosen in a consistent manner;
(e) it captures name-related basis risk and should in particular be sensitive to material idiosyncratic differences between similar, but not identical, positions; and
(f) it captures event risk.
36. A Bank may choose to exclude from the use of its internal model for calculation of its specific risk Capital Requirement, those positions for which it calculates the Capital Requirement for specific Risk in accordance with relevant sections of Chapter 6 of BBR. A Bank may choose not to capture default and migration risks for debt instruments in its internal model where it is capturing those risks through internal models for incremental default and migration risk.