FRTB Standardised Approach (II): Delta, Vega and Curvature Charge for Sample Risk Class

For those who missed first article. Here you go: FRTB SA - The Bigger Picture

An Investment Bank would have thousands of trades in hundreds of books. Each of these trades are risky investments, that can give positive/negative returns. To assess this regularly, a bank is expected to review market risk factors & generate risks or sensitivities (which basically says that if a specific market move occurs because of an underlying risk factor, how much would the value of the investment rise or drop).

FRTB, under standardised approach, attempts to leverage these sensitivities or risks (under sensitivities based approach), that are already being generated by the bank to arrive at the 'capital charge' we discussed in first article.

Each of the risky investments sitting in trading books of the bank, would fall in one of the risk classes shown below i.e. GIRR or general interest rate risk, Equity, Commodity, FX, and 3 variants of credit spread risk.

Under each risk class, banks are expected to compute DELTA, VEGA, Curvature, DRC and RRAO Charge in FRTB SA implementation. In order to understand this, let us take a dummy oversimplified portfolio of trades that only has FX exposures.

DELTA Charge:

Banks already calculate FX_DELTA i.e. linear impact of change in FxSpot price for a given currency pair (risk factor) on their investments. So, how would the bank get to DELTA Capital Charge using Sensitivity Based Method for FX Risk Class? Well, just follow below steps.

Step 1: Calculate net sensitivity: just aggregate risk or sensitivity generated for each currency pair. Why net it? Well, it takes care of +ve and -ve positions taken on the same currency pair and gives a better view of the net position besides avoiding duplicating next steps on numerous trades in same currency pair.

Step 2: Calculate weighted sensitivity: The weighted sensitivity would simply be [FX_DELTA*Weight_Allocated]. Note that FRTB already provides weights for all currencies. It has determined that weight to be 15%. On certain specific currencies that weight assigned is slightly low i.e. 15/sqrt(2) = 10.61%. These currencies with lower weight are USD, EUR, JPY, AUD, GBP, CAD, CHF, MXN, CNY, NZD, RUB, HKD, SGD, TRY, KRW, SEK, ZAR, INR, NOK, BRL.

Guess why certain specified currencies have lower weight prescribed in FRTB?

Step 3: Aggregate the weighted sensitivities. First intra bucket and then inter (cross bucket). In FX Risk Class, each currency pair is its own bucket: so there is no need for further aggregation. But how can one aggregate between different buckets. Well, we need to use a correlation parameter which is set to 60% by FRTB for all currency pairs. I won't get into semantics of formula (which is readily available and provided for in BASEL guidelines).

VEGA Charge:

Vega risk is generated for only those products that have optionality embedded in it. It captures linear implied volatility risk. FX_Vega refers to the potential loss resulting from the change in value of implied volatility in its underlying. The FXVEGA (which I am sure is already computed in most banks) risk is used to calculate VEGA charge under FX Risk class in following steps:

Step 1: Calculate net sensitivity for each currency pair. You know how (same way as you did for DELTA).

Step 2: FRTB recommends VEGA maturity tenors to be one 0.5, 1, 3, 5 or 10 years. If a bank is already calculating FX_VEGA maturity bucket in more granular tenors, then they are may redistribute sensitivities among below tenors using linear interpolation.

Step 3: Calculate weighted sensitivity which should be read as multiply 'weight' with the number you arrived at in Step 2. However, FRTB tells you a way to arrive at weight as well. The Risk Weight (RW) is

RW = min(RiskWeightSigma * {sqrt(LiquidityHorizon)/sqrt(10)}, 100%)

What's Liquidity Horizon though? It is the time assumed to be required to exit or hedge a risk position without materially affecting market prices in stressed market conditions. The longer the liquidity horizon, the less liquid the risk factor is and thus the higher the capital requirements tend to be. FRTB has set the value of LH to be 40 or 60 I think.

The weighted sensitivity would then be RW*FX_Vega

Step 4: Intra bucket aggregation followed by inter bucket aggregation.

CURVATURE Charge:

It captures incremental non linear spot risk (which is missed in FX_DELTA). Curvature covers second-order risks arising from option positions in underlying exposed to very large moves. While DELTA alone reflects only small variation in the risk factor; curvature on the other hand, captures the effect of large variation i.e. large shock of the same risk factor.

Step 1: Shock the value (PV) of the trade by +/- 15% as well as +/-10.61% (recall that 15/sqrt(2)=10.61). If the CCY is one of the specified currency, the shocked value of +/-10.61% will be used. If the CCY is any other CCY then the shock value of +/-15% will be used in calculating CVR+ and CVR-.

Step 2: Calculate CVR+ and CVR-. This is done using below.

CVR+ = -(+vely Shocked PV - UnShockedPV - RW*DeltaSensitivity)

CVR-= -(-vely Shocked PV - UnShockedPV + RW*DeltaSensitivity)

Curious minds would wonder why is the above formula the way it is? Well, it's simple: In curvature risk charge we want to capture just the non linear risk which is not captured by DELTA. This is why we need to strip the DELTA off to avoid double counting of DELTA charge. The value of RW is again going to be either 15% or 10.61% depending upon which category of currency are we talking about (specified or not specified).

Step 3: Intra bucket Aggregation. Aggregate the up shift i.e. CVR+s and down shift i.e. CVR-s to bucket level i.e. individual currencies. Then select the highest loss for either up or down shift, by bucket.

Step 4: Inter bucket aggregation. This is done using correlation coefficient provided by regulator (which happens to be 60%).

One would notice that steps to arrive at capital charge in risk class and indicator (DELTA, VEGA and Curvature) revolves around what was suggested in first article of the series which basically says: Get the net sensitivity, distribute it across buckets, multiply sensitivities with respective weights and aggregate it at bucket level followed by inter bucket or cross bucket level. Having said this, there is another step left for each risk class and indicator which addresses correlation(s) that are bound to increase/decrease in times of financial stress.

FRTB recommends that dual aggregation process must be carried out 3 times per risk class and indicator, with three different correlation scenarios. Details on how different risk classes/buckets could be correlated are provided by FRTB.

Once we have DELTA Charge, Vega Charge, Curvature Charge, we must address charges associated with risk of default (DRC) followed by additional conservative charges associated with those products that have an exotic underlying (RRAO) demanding that we should add charges for them as they are not covered by SBA Charges or DRC charges. The same/similar steps are done for each Risk Class by the way. While I have discussed it for FX : similar steps are done for other risk classes too in order to arrive at the charge required to support risky investment trades in those classes.

I will discuss about DRC and RRAO in detail in next article in this series.

#frtb?#sba?#StandardisedApproach?#basel?#investmentbanking?#riskmanagement?#marketrisk?#bcbs?#bankingsector?#regulatorychange #delta #vega #curvature #capitalcharge