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Calculation

Cost Reduction

Having accurate risk means hedging correctly first time, reducing overall costs as the need to unwind and/or reverse incorrect hedges is minimised. Traditional Gamma can only estimate this risk accurately in parallel curve moves.

Take a simple trade - long a 2y2y swaption straddle
(For net 1 unit of gamma) the gamma exposure looks like the below table:

If the 2y point moved +4bps and the 4y point moved +2bps, then the 2y2y fwd move should be zero (discounting assumptions etc left aside for simplicity). 
Risk change and hence PL should both be zero but this is not the case for traditional gamma, showing a negative gamma PL for a long option, highlighting 2 problems:

  • Incorrect delta bucketing - correcting these "phantom" deltas reduces incorrect hedging 

  • Incorrect PL - incorrect risk bucketing leads to PLAT failures and higher capital costs

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Traditional gamma PL can be negative even though long the option

The errors are mainly due to second order risk being calculated incorrectly (not from the non-calculation of higher order risks).

 
Below, we highlight 5 benign scenarios and the delta changes and gamma PNLs calculated under both traditional gamma (TG) and PLATSON:

  1. Parallel shift (TG is accurate as per the implicit assumption)

  2. Bear Flatten

  3. Bear Steepen

  4. Bull Flatten

  5. Bull Steepen

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The delta section (in green) shows that for non-parallel moves, traditional gamma achieves correct Net Delta but incorrect Gross Delta due to incorrect bucketing.  This is the most significant cause of the non-linear PL errors.

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Gross Delta Bucketing Error (%) is defined as ABS ( Gross Error / Gross delta )

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On the above scenarios where 2s4s flattens/steepens <1bp, PLATSON gamma gives improved gross delta predicts of 25-100% (in yellow).

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The simple trade was modelled over the last 1 year of USD rate moves, during which 2y and 4y swap were correlated at 99% and a (generous) 50% tolerance for Gross Delta Bucketing Error has been allowed.  Only on the days when the error exceeds this is a charge of 0.05 basis points applied to the incorrect delta (to account for brokerage, operations, bid/offer, clearing fees, compression fees etc)

For the simple case of 1bn USD 2y2y ATM straddle, 66k USD is bled - on a daily basis this is unlikely to be picked up but across a complex portfolio, can add up to significant haemorrhaging over the year. 

Extended to the sample portfolio, cost savings rise to 800k

Capital Savings

Reduction of non-linear errors by 95%

PL inaccuracies will drive banks onto higher capital models (SA vs IMA - see the PLATSON FRTB primer for further information) under new BIS (FRTB) regulations

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The PLATSON Solution can significantly increase the pass rate of PLAT for all manner of portfolios without having to resort to adding arbitrary delta or vega overlays to the portfolio.

 
For example the results of the  2y2y straddle have been run through the three proposed PLAT and traditional gamma results compared with those using the PLATSON solution.  Results were run for various levels of delta, vega and gamma hedging. 

For ATM straddles, traditional gamma can generally pass PLAT although errors do start to creep in once the vega is hedged.

 

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The PLATSON solution starts to show significant value on structures such as 2y2y straddle ATM+50 vs ATM+115 1x2 USD payer spread.  Traditional gamma calculation methods fail at almost every hedging level chosen - PLATSON comfortably passes at all hedging levels chosen

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