# M2MO: Modélisation Aléatoire, Finance et Data Science

Master en statistique, probabilités et finance - Université Paris 7 - Paris Diderot

## XVA analysis

 Lecturer: S. Crépey Period: Term 3 ECTS: 3 Hourly volume: 3 hours per week

Since 2008, investment banks compute various X-valuation adjustments (XVAs) to assess counterparty risk and its funding and capital implications. 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. The course will provide an up-to-date covering 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 and neural net regressions).

Outline

1 The XVA cost-of-capital approach in a static setup

2 The XVA cost-of-capital approach in continuous time

3 XVA analysis of  bilateral trade portfolios

4 XVA computational strategies: nested Monte Carlo vs. neural net regressions

5 XVA analysis of centrally cleared portfolios

References:   Related material on https://perso.lpsm.paris/~crepey/

Keywords:  credit valuation adjustment (CVA), funding valuation adjustment (FVA), capital valuation adjustment (KVA), neural net regressions and quantile regressions, central counterparties (CCP).

Prior knowledge:  Stochastic analysis, mathematical finance, numerical finance at MSc level. Some knowledge of corporate finance or programming skills in python and/or C++  are also useful but can be acquired “on the job”.

Assessment:  Written examination or programming projects to be delivered as python jupyter notebooks running under Google Colab