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Context 1
... in the above equations to the bank survival measure R based on Lemma 3.3 shows that the corresponding fixed point problem is in fact well-posed and yields explicit formulas for all the quantities at hand. Table 2 hold and we have ...Context 2
... only XVA definitions and explicit formulas that change with respect to Tables 1 and 2 (on top of C and F generalized as above) are the ones for CCVA and CMVA, the way detailed in Tables 3 and 4. Moreover, ...Context 3
... cr and ρ mkt , but a significant positive impact of ρ wwr . This is understandable for the sensitivity to ρ cr and ρ mkt as, apart for modulations of the measure with respect to which each individual CCVA is assessed, the CCVA aggregated over clearing members is essentially an expectation of the CCP loss L (cf. the first line of Table 2 ). The individual CCVAs (as per the first line of Table 2 ) of each clearing member, however, may depend on ρ cr and ρ mkt (on top of ρ wwr ) in a strong and nontrivial manner, via the allocation coefficient µ. ...Context 4
... is understandable for the sensitivity to ρ cr and ρ mkt as, apart for modulations of the measure with respect to which each individual CCVA is assessed, the CCVA aggregated over clearing members is essentially an expectation of the CCP loss L (cf. the first line of Table 2 ). The individual CCVAs (as per the first line of Table 2 ) of each clearing member, however, may depend on ρ cr and ρ mkt (on top of ρ wwr ) in a strong and nontrivial manner, via the allocation coefficient µ. Total KVA overall members ...Context 5
... 0.0251 0.3557 Table 12: Standard deviation across surviving members * of the ∆XVA * for the example with 1 CCP and 20 members, assuming an instant default of CM0 at time 0. ...Citations
... When a clearing member defaults, the CCP can hedge and auction or liquidate its positions. The counterparty credit risk cost of auctioning has been analyzed in terms of XVA metrics in Bastide, Crépey, Drapeau, and Tadese (2023). In this work we assess the costs of hedging or liquidating. ...
... If a clearing member d defaults, its client deals and their static hedge are ported as a package to a surviving clearing member (right panel in Figure 2). As market risk is perfectly hedged throughout, such porting has no market impact, but entails a transfer of counterparty credit risk that can be quantified by XVA costs as per Bastide et al. (2023, Section 7) (second row in Table 11). ...
... The purpose of this part is to provide a bridge from the equilibrium setup of Sections 2-5 to the XVA setup of Bastide et al. (2023), so that we are able to provide an overall FTP (6.3) quantifying the market but also credit costs of a given default resolution strategy. We leave for future research the extension of the approach of this paper to a setup where not only the market costs, but also the credit costs, would be treated endogenously as part of a global (or perhaps two-stage 16 ) equilibrium, ideally in the setup of a dynamic model. ...
For vanilla derivatives that constitute the bulk of investment banks' hedging portfolios, central clearing through central counterparties (CCPs) has become hegemonic. A key mandate of a CCP is to provide an efficient and proper clearing member default resolution procedure. When a clearing member defaults, the CCP can hedge and auction or liquidate its positions. The counterparty credit risk cost of auctioning has been analyzed in terms of XVA metrics in Bastide, Cr{é}pey, Drapeau, and Tadese (2023). In this work we assess the costs of hedging or liquidating. This is done by comparing pre- and post-default market equilibria, using a Radner equilibrium approach for portfolio allocation and price discovery in each case. We show that the Radner equilibria uniquely exist and we provide both analytical and numerical solutions for the latter in elliptically distributed markets. Using such tools, a CCP could decide rationally on which market to hedge and auction or liquidate defaulted portfolios.
