The multiplication factor was considered to be too high, possibly undermining incentives to use the models approach.

There should be more flexibility built into the modelling parameters (e.g., the constraints on the method of recognising correlations and the dual observation period).

More guidance was needed as to how the so-called "plus factor" would be implemented in practice.

There should be recognition of the specific risk component captured by a bank's model. A number of commenters favoured the removal of the constraint considered in the April 1995 consultative document, which stated that the total specific risk charge applied to debt securities or to equities could not be less than half the specific risk charges calculated according to the standardised approach.

7. The Committee has carefully reviewed these and the other comments received. It has concluded that the overall approach of the April 1995 proposal remains appropriate. In particular, it reaffirms the strict qualitative standards for the risk management process which will apply to banks that base their capital requirements on the results of internal models. However, in light of the comments received, the Committee has made some refinements to the quantitative parameters, and these are summarised below. The final language adopted by the Committee is presented in Part B of the Amendment to the Accord. (a) Multiplication factor

8. As mentioned above, a significant number of respondents questioned the proposed multiplication factor. Some argued that banks' models measured risk with a high degree of precision and that a factor was therefore not necessary. The Committee accepts that banks' internal models provide a valuable starting point for measuring the riskiness of a bank's trading portfolio. However, this daily value-at-risk estimate then needs to be translated into a capital charge that provides a sufficient cushion for cumulative losses arising from adverse market conditions over an extended period of time. Many banks themselves employ relatively conservative assumptions for the purpose of allocating capital internally, including methods such as scaling up their value-at-risk estimate.

9. The multiplication factor is also designed to account for potential weaknesses in the modelling process. Such weaknesses exist because:

Market price movements often display patterns (such as "fat tails") that differ from the statistical simplifications used in modelling (such as the assumption of a "normal distribution").

The past is not always a good approximation of the future (for example volatilities and correlations can change abruptly).

Value-at-risk estimates are typically based on end-of-day positions and generally do not take account of intra-day trading risk.

Models cannot adequately capture event risk arising from exceptional market circumstances.

Many models rely on simplifying assumptions to value the positions in the portfolio, particularly in the case of complex instruments such as options.

When seen in the context of the other quantitative parameters, the Committee has concluded that a multiplication factor of 3 provides an appropriate and reasonable level of capital coverage to address these prudential concerns.

(b) Additional flexibility in parameters

10. In reviewing the comments, the Committee has given careful consideration as to how best to balance the need to preserve the integrity and flexibility of banks' internal models against the need to ensure a minimum level of prudence, transparency, and consistency of the capital requirement across banks.

11. Against this background, the Committee has concluded that the costs of a dual observation period, on which banks were asked to comment in the consultative document, generally outweigh the potential benefits. However, the Committee has retained the minimum one year constraint on the length of the observation period. This constraint is straightforward to implement, and it strikes a reasonable balance between the relative advantages and disadvantages of a shorter and a longer observation period. The disadvantage of a shorter observation period is that it captures only recent market "shocks" and that it could lead to a very low measure of risk if it coincides with an unusually long stable period in the markets. Conversely, the disadvantage of a longer time horizon is that it does not respond rapidly to changes in market conditions. Tests conducted by the Committee suggest that a one year floor on the observation period can contribute significantly to reducing the variability in measured value-at-risk that may occur for a given set of positions across banks.

12. The Committee has also reviewed the question of how to address different weighting schemes for the observation period. It concludes that banks should have some flexibility in this area, subject to the constraint that the "effective" observation period be at least one year.

13. The Committee reaffirms the appropriateness of requiring banks to calculate value-at-risk based on an instantaneous shock equivalent to a 10 day move in prices (the holding period). While it would of course be possible to define different price shocks for different classes of instruments, the approach chosen by the Committee provides a straightforward method for addressing the risk that portfolio losses can build up over a period of time greater than a day. To limit industry burden, banks will be allowed to scale up or down their value-at-risk measure to arrive at the required 10 day holding period. Moreover, the Committee has decided to allow more flexibility than indicated in the April 1995 proposal in the treatment of instruments with non-linear risks. Thus, banks will be permitted to scale up their one day value-at-risk measure for options by the square root of ten for a certain period of time after the internal models approach takes effect at end-1997. They should, however, take additional steps to assess the risk in their portfolio over a large number of possible price movements applying, for example, Monte Carlo simulations and/or stress testing. Moreover, the ultimate standard for banks to achieve over time remains unchanged, namely the measurement of non-linearity through a ten-day price shock with full revaluation of positions, but with some flexibility as to the specific methodology to be used.

14. The Committee has reviewed the treatment proposed in the April 1995 consultative document whereby banks could recognise correlation effects within broad risk factor categories (i.e., interest rates, exchange rates, equity prices and commodity prices, including related options volatilities in each risk factor category), but would have to aggregate value-at-risk numbers across risk factor categories on a simple sum basis. After careful consideration, the Committee has concluded that it would be appropriate to permit a bank to recognise empirical correlations not only within broad risk factor categories, but also across risk factor categories, provided that the supervisory authority is satisfied the bank's system for measuring correlations is sound and implemented with integrity. In particular, as discussed in Part B of the Amendment to the Accord, banks should reassess their data sets whenever market prices are subject to material changes, and they must perform stress tests on the stability of correlations. Recognising correlations across risk factor categories should provide incentives for institutions to diversify their trading activities, thus reducing risk.

(c) The plus factor

15. In the April 1995 consultative document, the Committee announced its intention to add to the minimum multiplication factor a so-called plus factor based on the outcome of backtesting, that is, an ex-post comparison of the risk measure generated by the model against actual daily changes in portfolio value. Commenters generally welcomed the concept that there should be an incentive to construct models with good predictive quality, but called for more clarification about how this would be implemented in practice.

16. The criteria adopted by the Committee for defining the plus factor are presented in Section B.4 (j) of the Amendment to the Accord and in the document, Supervisory Framework for the Use of "Backtesting" in Conjunction with the Internal Models Approach to Market Risk Capital Requirements. If the backtesting results are satisfactory and the bank meets all of the qualitative standards set out in the Amendment to the Accord, the plus factor will be zero. The Committee believes that the approach adopted strikes a balance between recognition of the potential limitations of backtesting and the need to put in place a clear and consistent framework that contains incentives to ensure that banks model market risk with integrity. At the same time, the Committee recognises that the techniques for backtesting are still evolving, and it is committed to incorporating important new developments in this area into its framework.

(d) Treatment of specific risk

17. The capital framework for market risk is based on the so-called "building block" approach that separates general market risk arising from movements in broad risk factors from the specific risk associated with individual securities positions. The internal models approach was developed principally to provide an alternative to the general market risk component of the standardised approach. However, the April 1995 consultative document allowed some scope for the internal modelling of specific risk and invited comment on how the specific risk component was being or could be measured for capital purposes.

18. Industry comments indicate that banks' internal models may capture certain elements of specific risk, for example where each equity is modelled as an individual risk factor. However, it appears that other key elements of specific risk such as event or default risk are generally not captured by banks' internal models. Banks provided little evidence in the comment process that their models were capturing specific risk in respect of debt securities.

19. There is a willingness to give some recognition to banks whose models capture specific risk and to put in place incentives to further improve upon these methodologies. On the other hand, there needs to be a prudential cushion to address the concern that practice is still developing in this area and that an industry consensus has not yet emerged about how best to model certain elements of specific risk. The Committee has accordingly decided to retain the treatment proposed in the April 1995 consultative document, whereby a modelled treatment of specific risk would be allowed subject to an overall floor on the specific risk charge equal to 50% of the specific risk charge applicable under the standardised approach. Banks whose models take little or no account of specific risk will be subject to the full specific risk charges of the standardised approach. For example, banks with models that are limited to capturing movements in equity indices, or to the spread between the interbank or corporate yield curves and that on government securities, should expect to receive the full specific risk charges of the standardised approach.

20. Should the industry come forward with a reasonable methodology for measuring specific risk in the context of the internal models approach, the Committee is prepared to reconsider its approach in this area.

(e) Summary

21. The Committee notes that the use of proprietary in-house models to measure market risk for supervisory capital purposes represents a significant innovation in supervisory methods. Moreover, many internationally active banks are themselves in the process of gaining experience with the use of risk measurement and management techniques based on the value-at-risk approach. In order to gain additional information and comfort with the results produced by internal models, supervisory authorities reserve the right to require banks wishing to use internal models to perform testing exercises and to provide any other information necessary to check the validity of banks' models. All banks that wish to use models should therefore have the capability to evaluate a test portfolio.