Minicourse ‘XVA Analysis’
By Stéphane Crépey, professor Université Paris Cité /LPSM

Since 2008,  XVAs deeply affect the derivative pricing task by making it global (portfolio-wide), nonlinear, and entity dependent. A proper financial understanding of even the first generation XVAs (CVA, DVA, and FVA, where C sits for credit, D for debt, and F for funding) points out to the distinction between firm and shareholder valuation, which mathematically goes to enlargement of filtration and singular probability change. Second generation XVAs involve not only conditional expectations (i.e. prices), but also conditional risk measures (value-at-risk and expected shortfall) for MVA (margin valuation adjustment) and KVA (capital valuation adjustment) computations. This minicourse will provide a survey of the XVA universe and of the embedded risk measure issues, from the triple angle of finance (wealth transfers), stochastic analysis (enlargement of filtration and backward SDEs), and computations (nested Monte Carlo versus neural net regressions and quantile regressions implemented in pytorch with GPU acceleration).