Higher Order Derivatives Analytics
Case Study
A relatively well hedged sample portfolio (hedging: delta 100%, vega 95% and gamma 75%) consisting of typical trades in a market making book with the below delta, vega, gamma risks (in k USD) is run over a year of daily market moves (Apr2017-Apr2018 USD data - fairly benign volatility) using both Traditional Gamma and the PLATSON solution and 2 tests were performed on each method:
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Allowing for a 50% margin of error for predicted delta, how much would it cost to rehedge the portfolio to the the real delta.
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Will the predicted PL be accurate enough to pass PLAT under FRTB regulations
The results show that
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Compared to using Traditional Gamma, the PLATSON solution achieved 800k of cost reductions (from having delta bucketed correctly)
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Traditional gamma would fail PLAT whilst PLATSON passed PLAT for every type of portfolio, saving 800k in capital charges.
Incorrect hedging costs
Even if we allow TG a 50% margin of error in risk estimation, this can cost 815k USD p.a. from the gamma errors alone.
Errors arise due to the assumptions (eg parallel curve moves) and shortcuts (due to computational time restraints) made when estimating risk generated by second order derivatives (gamma, volga, vanna).
Further details are on the Calculation page
Capital Savings
The PLAT test results show that using traditional calculations PLAT will be failed (in red) but if the PLATSON solution is used, the tests are comfortably passed allowing IMA capitalisation as opposed to SA, reducing capital costs by 854k USD p.a.
Sample Portfolio and pre-hedging delta, gamma, vega
