Iggaak and Hiram Finance bridged the gap between XVA valuations and hedging valuations to help a bank deal with P&L volatility.
The Bank actively manages and hedges CVA and FVA with liquid instruments in the interbank market. The XVA P&l post hedge is highly volatile. The P&l needs to be explained and the hedging strategy needs to be optimized.
Several strategies are possible such as no hedge, rate hedge and rate+CDS hedge. Furthermore, the XVA payout includes optionality and is highly non-linear, with gamma and cross-gamma sensitivities.
In order to determine which strategy best resists arbitrary market movements, we apply a diffusion to the book with its dynamic hedge, applying a process for rates and a process for CDS. We calculate the variance of the PL of the package over this period, for each hedge strategy. The minimum variance strategy will be preferred.
Going forward, the proposed tool will help to better select hedging instruments and to better understand the residual volatility.
The P&l variances of the book can now be separated into two categories:
* The variance due to the imperfection of the hedges (non-instantaneous deltas, non-readjusted swaption strikes, etc…)
* The variance from non-hedgeable risks (cross-Gamma, cross-Vanna, etc.).