December 19th, 2015, 2:23 pm
under the new FRTB regulatory regime ,P&L attribution is one of the tools in conjunction with backtesting that must meet rigid criteria for desk level performance and approval to be included in the application for the use of Internal models at desk level ,i.e FI must meet the rigid requirements at desk level (whatever that means...vague ) in order use internal models at desk level under the proposed FRTB guidelines which are set to be complete and the official text to be out in january 2016 , FI need to reconcile actual P&L to theoretical P&L by meeting a regulatory proposed threshold,which is difficult to satisfy :let sigma_actual ,sigma_theoretical and sigma(Theoretical -Actual ) be the respective P&L vols ,your theoretical p&L should be a very good predictor of your actual P&L and this hold if the correlation between the 2 p&l's is at least 90% ! ....it follows thatsigma_(theoretical -Actual ) = sqrt( ( sigma^2(theoretical ) - 2 * correlation (sigma_(actual),sigma_(theoretical))*sigma(actual)*sigma_(theoretical)+sigma^2_(actual))if we assume that sigma_(actual) = sigma_(theoretical) rearranging and factoring we have :sigma_(theoretical -Actual)/sigma(actual) = sqrt( ( 2-2 * rho(actual,theoretical)),so to meet the rigid threshold (proposed) : then (sigma_(theoretical-actual)/sigma_(actual))^2 <20% ,we need rho to be >90%