XVA analysis, risk measures and applications to centrally cleared trading.

Summary This thesis addresses various issues related to collateral management in the context of centralized trading through clearing houses. First, we present the notions of capital cost and funding cost for a bank, by placing them in an elementary Black-Scholes framework where the payoff of a standard call takes the place of a counterparty default exposure. We assume that the bank only imperfectly hedges this call and faces a funding cost higher than the risk-free rate, hence the FVA and KVA pricing corrections with respect to the Black-Scholes price. We then focus on the costs that a bank faces when trading in a CCP. To this end, we transpose the XVA framework of bilateral trading to centralized trading. The total cost for a member to trade through a CCP is thus decomposed into a CVA corresponding to the cost for the member to replenish its contribution to the guarantee fund in case of losses due to defaults by other members, an MVA corresponding to 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. We then question the regulatory assumptions previously used, looking at alternatives in which members would use a third party for their initial margin, who would post the margin in the member's place in exchange for a fee. We also consider a method of calculating the guarantee fund and its allocation that takes into account the risk of the chamber in the sense of the fluctuations of its P&L over the following year, as it results from the combination of the market risk and the default risk of the members. Finally, we propose the application of multivariate risk measure methodologies for the calculation of members' margins and/or guarantee funds. 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 (e.g., but not necessarily the positions of the members of a CCP), but also to their dependence.