  Banks must manage their trading books, not just value them. Pricing includes
valuation adjustments collectively known as XVA (at least credit, funding,
capital and tax), so management must also include XVA. In trading book
management we focus on pricing, hedging, and allocation of prices or hedging
costs to desks on an individual trade basis. We show how to combine three
technical elements to radically simplify XVA management, both in terms of the
calculations, and the implementation of the calculations. The three technical
elements are: trade-level regression; analytic computation of sensitivities;
and global conditioning. All three are required to obtain the radical
efficiency gains and implementation simplification. Moreover, many of the
calculations are inherently parallel and suitable for GPU implementation. The
resulting methodology for XVA management is sufficiently general that we can
cover pricing, first- and second-order sensitivities, and exact trade-level
allocation of pricing and sensitivities within the same framework. Managing
incremental changes to portfolios exactly is also radically simplified.
