| (e) | Quantitative requirements relating to, among other things, minimum statistical parameters for the measurement of a bank's exposure to market risk |
| (i) | A bank that obtained the approval of the Registrar to adopt the internal models approach for the measurement of the bank's exposure to market risk arising from relevant positions held in the bank's trading book and/or banking book— |
| (A) | shall on a daily basis calculate the bank's value-at-risk ("VaR") amount, which VaR amount— |
| (i) | shall be based on a 99th percentile, one-tailed confidence interval; |
| (ii) | shall be based on an instantaneous price shock equivalent to a ten day movement in market prices, that is, a minimum "holding period" of ten trading days, provided that when the bank is unable to determine the required value-at-risk amounts based on a ten day holding period, and the bank's VaR amount is based on a holding period of less than ten trading days, the bank shall scale up the relevant calculated VaR amounts to ten trading days by making use of, for example, the relevant square root of time formula for the treatment of options, provided that a bank that does make use of such square root of time formula to scale up its relevant calculated VaR amount to ten trading days shall periodically demonstrate to the satisfaction of the Registrar the continued reasonableness of the said calculation; |
| (iii) | shall be based on a historical observation period or sample period of no less than one year, provided that— |
| (aa) | the Registrar may require a bank to calculate its value-at-risk amount based on a shorter observation period when, in the opinion of the Registrar, the said calculation is justified by a significant upsurge in market price volatility; |
| (bb) | a bank that uses a weighting scheme or other methods in respect of the historical observation period shall ensure that the "effective" observation period is no less than one year, that is, the weighted average time lag of the individual observations shall not be less than six months, or the method used by the bank shall result in a required amount of capital and reserve funds at least as conservative as the amount calculated in accordance with the requirement related to the aforesaid observation period; |
| (B) | shall update its data sets no less frequently than once every month, provided that the bank shall reassess the relevant data sets whenever market prices are subject to material changes, that is, the bank's internal processes related to the updating of data sets shall be sufficiently flexible to allow for the frequent updating of all relevant data sets; |
| (C) | may recognise empirical correlations within broad risk categories such as interest rates, exchange rates, equity prices and commodity prices, including related option volatilities in respect of each relevant risk-factor category, provided that, subject to the prior written approval of and such further conditions as may be specified in writing by the Registrar, a bank may also recognise empirical correlations across broad risk factor categories; |
| (D) | shall have in place a robust risk measurement system, which risk measurement system— |
| (i) | among other things, shall duly capture the unique risks associated with options within each of the specified broad categories of risk, that is, the bank's model shall accurately capture the non-linear price characteristics associated with option positions, provided that— |
| (aa) | ultimately the bank shall move towards the application of a full 10-day price shock to option positions or positions that display option-like characteristics; |
| (bb) | the Registrar may require a bank to adjust its capital measure for option risk through the application of methods such as periodic simulations or stress testing, the results of which simulations or stress testing shall be duly documented; |
| (ii) | shall contain a set of risk factors that captures the volatilities of the rates and prices underlying all relevant option positions, that is, vega risk, provided that a bank with large and/or complex option portfolios shall have in place detailed specifications of the relevant volatilities, that is, based on the relevant different maturities of the bank's option positions, the bank shall measure the relevant volatilities relating to all relevant option positions. |
| (E) | shall, in addition to the aforesaid VaR calculation, calculate a stressed value-at-risk ( "sVaR ") measure, which sVaR— |
| (i) | replicates a value-at-risk calculation that would be generated on the bank's current portfolio if the relevant market factors were subject to a period of significant stress; |
| (ii) | shall be based on a 10-day, 99th percentile, one-tailed confidence interval value-at-risk measure of the bank's current portfolio, with model inputs calibrated to historical data from a continuous 12-month period of significant financial stress relevant to the bank's portfolio, such as a 12-month period relating to significant losses incurred during the 2007/2008 financial market crisis, which period shall regularly be reviewed by the bank; |
| (iii) | shall be calculated at least once every week; |
| (iv) | calculation and any related matter, including the relevant 12-month period of significant financial stress, shall be subject to such further conditions or requirements as may be specified in writing by the Registrar; |
| (ii) | No particular type of model is prescribed, that is, a bank may, at the discretion of the bank, for example, use models based on variance-covariance matrices, historical simulations, or Monte Carlo simulations, provided that the model used by the bank shall capture all relevant material risks incurred by the bank. |
| (iii) | On a daily basis, as a minimum, subject to any relevant requirement related to the calculation and/or maintenance of a minimum required amount of capital and reserve funds that may be specified in the form BA 700 or in regulation 38 of these Regulations, a bank that obtained the approval of the Registrar to adopt the internal models approach for the measurement of the bank's exposure to market risk shall maintain a capital requirement in respect of the said exposure, equal to the sum of— |
| (i) | the previous day's VaR amount, that is, VaRt-i, measured in accordance with the relevant parameters and requirements specified in this subregulation (8); or |
| (ii) | the average amount of the daily VaR amount, that is, VaRavg, calculated in accordance with the relevant parameters and requirements specified in this subregulation (8), in respect of each of the preceding sixty business days, multiplied by the multiplication factor, mc, envisaged in subparagraph (iv) below; |
and, or plus—
(B) the higher of—
| (i) | the latest available sVaR amount, that is, sVaRt-1, measured in accordance with the relevant parameters and requirements specified in this subregulation (8); or |
| (ii) | the average amount of the sVaR amount, that is, sVaRavg, calculated in accordance with the relevant parameters and requirements specified in this subregulation (8), in respect of the preceding sixty business days, multiplied by the multiplication factor, ms, envisaged in subparagraph (iv) below; |
that is, the bank's required amount of capital and reserve funds shall be equal to:
max{VaRt-1; mc x VaRavg} + max{sVaRt-i; ms x sVaRavg}
| (iv) | Based on, among other things, the Registrar's assessment of the quality of a bank's risk management system and related processes, the Registrar shall specify in writing the aforesaid multiplication factors, mc and ms, which multiplication factors shall in no case be less than three, and a "plusfactor", which plus-factor— |
| (A) | shall directly relate to the ex-post performance of the bank's model, thereby providing a built-in incentive for the bank to maintain or improve the predictive quality of the model; |
| (B) | based on the outcome of backtesting, may range between zero and one, that is, when the backtesting results of the relevant bank— |
| (i) | are satisfactory, and the bank complies with all the qualitative standards specified in regulation 39(14)(b), the plus factor may be equal to zero; or |
| (ii) | fall into the red zone specified by the Registrar from time to time, the multiplication factor applicable to the said bank's model shall automatically increase by one, to four. |
| (C) | shall be based on the outcome of backtesting in respect of the bank's VaR amount, and not the bank's sVaR amount. |
