XVA Analysis, Risk Measures and Applications to Centrally Cleared Trading

Abstract : This thesis deals with various issues related to collateral management in the context of centralized trading through central clearing houses. In the first place, we present the notions of cost of capital and funding cost for a bank, placing them in an elementary Black–Scholes framework where the payoff of a standard call is used as the exposure at default of a counterparty. It is assumed that the bank can’t perfectly hedge this call and must face with a funding cost higher than the risk free rate, hence pricing corrections of the FVA and KVA type appear in top of the Black–Scholes price. Then, we look at the different costs that a bank has to face when trading in the CCP context. To this end, we transpose the well-known XVA analysis framework from the bilateral trading world to the central clearing one. The total cost for a member trading through a CCP is thus decomposed into a CVA corresponding to the cost for the member to reimburse its contribution to the guarantee fund in the event of losses due to the defaults of other members, a MVA which is the cost of financing its initial margin and a KVA corresponding to the cost of capital put at risk by the member in the form of its contribution to the guarantee fund. Afterwards, we question the previously used regulatory assumptions, focusing on alternatives in which members would borrow their initial margin to a third party who would post the margin instead of the member himself, and this, in exchange for remuneration. We also consider a method of computing the guarantee fund and its allocation taking into account the risk of the CCP in the sense of fluctuations of its P&L over the following year, as it results from the market risk and the counterparty risk of the members. Finally, we propose the application of multivariate risk measure methodologies for the computation of margins and/or the CCP guarantee fund. We introduce a notion of systemic risk measures in the sense that they are sensitive not only to the marginal risks of the components of a financial system (for example, but not necessarily the positions of the members of a CCP) but also to the dependence of their components.
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Yannick Armenti. XVA Analysis, Risk Measures and Applications to Centrally Cleared Trading. Computational Finance [q-fin.CP]. Université Paris Saclay; Université d'Evry Val d'Essonne, 2017. English. ⟨tel-01653773⟩

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