Last updated on 6 September 2016

New standardised method to calculate market risk capital under FRTB is primarily based on risk sensitivities also known as *sensitivities based approach (SBA)*. Unlike current rules, new rules require all banks to calculate market risk capital charge using standardised method. It is not confirmed yet if capital requirements calculated using standardised method will act as a floor for the banks who have approval to use internal model for calculating market risk capital. Market risk capital using standardised approach is simply a sum of

**capital charge**with respect to risk sensitivities (Delta, Vega and Curvature);**default risk charge**which captures jump-to-default risk for default risk of non-securitisations, securitisations (non-correlation trading portfolio) and securitisations (correlation trading portfolio);**residual risk add-on**to account for those market risks which can not be captured through first two items.

### Steps for calculating capital charge for risk sensitivities

- Calculate capital charge for each
**sensitivity**(*Delta, Vega and Curvature*)**risk class**under three different**correlation scenarios**; - For each correlation scenario, capital charge at the portfolio level is calculated as a simple sum of the capital charge for each risk class;
- Final portfolio level capital charge is calculated as a maximum of the three scenario related portfolio level capital charge.

Mathematically, this can be represented as

**K _{p} = max(K_{H}, K_{M}, K_{L}) **where

**K _{p }**is a capital charge for the portfolio;

**K**is a capital charge for the portfolio under high correlations scenario;

_{H }**K**is a capital charge for the portfolio under medium correlations scenario and;

_{M }**K**is a capital charge for the portfolio under lowcorrelations scenario;

_{L }**K _{s} = ∑_{r }(Delta_{r} + Vega_{r} + Curvature_{r}) **where

**s** represents one of high, medium or low correlation scenario;

**r** represents one of seven risk classes – *General Interest Rate Risk, FX Risk, Commodities Risk, Credit Spread Risk – Non Securitisation, Credit Spread Risk – Securitisation (Correlation Trading), Credit Spread Risk – Securitisation (Non-Correlation Trading) and Equity Risk*.

Delta, Vega and Curvature risk capital charges are discussed in later posts.

It can be seen from the second equation that no diversification benefit has been allowed between risk classes and through the first equation BCBS ensures that the capital charge is set aside for the worst scenario for the bank.

### Risk Class

As discussed above, sensitivity based capital charge is calculated at the **risk class** level. Picture below shows seven risk classes along with an example which introduces an hierarchy for aggregation purposes.

Consider a portfolio of G7 Rates which typically will have interest rate swaps, cross-currency swaps and interest rate options in G7 currencies. In case of GIRR risk class, currencies are referred as **Bucket** which are exposed to Delta, Vega and Curvature **risk factors**.

**GIRR Delta Risk Factor**– This has two dimensions – curve type and tenor. So USD Libor 1m and USD OIS 1m are two different risk factors. Similarly, onshore and offshore currency curves are considered different curves.**GIRR Vega Risk Factor**– Implied volatility of options. By nature this will have two dimensions as well – maturity of the option and residual maturity of the underlying. In above picture, 5y option on a 10y swap is one risk factor for a USD Swaption.**GIRR Curvature Risk Factor**– Similar to GIRR Delta Risk factor except that tenor is not the dimension i.e. curvature risk is calculated for a whole curve like Libor or OIS. This is achieved by applying a parallel shock to the curve.

For other risk classes these risk factors are defined in detail in the official documentation (paras 59-66) and are fairly straight forward. For example, FX Delta (and Curvature) risk factor is an exchange rate between the exposure currency and the reporting currency, FX Vega risk factor is an implied volatility of the currency pair for each option maturity.

In my next post, I will discuss Delta risk charge with an example in one of the risk classes.

## sangwook

very good summary on the subject

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## Anshu Bhadauria

Have you checked articles on http://www.risk.net?