the bank is operating in (see Too big to fail). The discipline is, as outlined, simultaneously concerned with (i) managing, and as necessary hedging, the various positions held by the institution — both trading positions and long term exposures; and (ii) calculating and monitoring the resultant economic capital, as well as the regulatory capital under Basel III - with the latter as a floor. The calculations here are mathematically sophisticated, and within the domain of quantitative finance. Broadly, calculations are built for (i) on the "Greeks", the sensitivity of the price of a derivative to a change in its underlying parameters, as well as on the various other measures of exposure to market factors, such as DV01 for the sensitivity of a bond or swap to interest rates; and for (ii) on value at risk, or "VaR", an estimate of how much the investment or area in question might lose with a given probability in a set time period, and the bank holds economic “risk capital” correspondingly. The regulatory capital quantum is calculated via specified formulae: risk weighting the exposures per highly standardized asset-categorizations, applying the aside frameworks, and the resultant capital - at least 12.9% of these Risk-weighted assets - must then be held in specific "tiers" and is measured correspondingly. In certain cases, banks are allowed to use their own estimated risk parameters here; these "internal ratings-based models" typically result in less required capital, but at the same time are subject to strict minimum conditions and disclosure requirements. As the financial crisis exposed holes in the mechanisms used for hedging, the methodologies employed have had to evolve (see FRTB, and ): A core technique continues to be Value at Risk — applying the traditional parametric and "Historical" approaches — but now supplemented with the more sophisticated Conditional value at risk / expected shortfall, Tail value at risk, and Extreme value theory (and PFE and EE for regulatory). For the underlying mathematics, these may utilize mixture models, PCA, volatility clustering, copulas, and other techniques. For the daily direct analysis of the positions at the desk level, as a standard, measurement of the Greeks now inheres the volatility surface — through local- or stochastic volatility models — while re interest rates, discounting and analytics are under a "multi-curve framework". Derivative pricing now embeds credit and other considerations through the CVA and XVA "valuation adjustments". Additional to these, are various forms