Credit, funding, margin, and capital valuation adjustments for bilateral portfolios

Abstract

which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Abstract We apply to the concrete setup of a bank engaged into bilateral trade portfolios the XVA theoretical framework of Albanese and Crépey (2017), whereby so-called contra-liabilities and cost of capital are charged by the bank to its clients, on top of the fair valuation of counterparty risk, in order to account for the incompleteness of this risk. The transfer of the residual reserve credit capital from shareholders to creditors at bank default results in a unilateral CVA, consistent with the regulatory requirement that capital should not diminish as an effect of the sole deterioration of the bank credit spread. Our funding cost for variation margin (FVA) is defined asymmetrically since there is no benefit in holding excess capital in the future. Capital is fungible as a source of funding for variation margin, causing a material FVA reduction. We introduce a specialist initial margin lending scheme that drastically reduces the funding cost for initial margin (MVA). Our capital valuation adjustment (KVA) is defined as a risk premium, i.e. the cost of remunerating shareholder capital at risk at some hurdle rate. Keywords

XVA Analysis From the Balance Sheet

“…From a computational point of view, this paper opens the way to second generation XVA GPU implementation. The first generation consisted of nested Monte Carlo implemented by explicit CUDA programming on GPUs (see Albanese, Caenazzo, and Crépey (2017), Abbas-Turki, Diallo, and Crépey ( 20The second generation takes advantage of GPUs leveraging via pre-coded CUDA/AAD deep learning packages that are used for the XVA embedded regression and quantile regression task. Compared to a regulatory capital based KVA approach, an economic capital based KVA approach is then not only conceptually more satisfying, but also simpler to implement.…”

“…Remark 3.4 The rationale for funding FVA but not MVA from CA + max(EC, KVA) is set out before Equation (15) in Albanese, Caenazzo, and Crépey (2017).…”

Xva Principles, Nested Monte Carlo Strategies, and Gpu Optimizations

“…In this section we recall the XVA principles of , to which we refer the reader for more details. See also the companion papers by Albanese, Caenazzo, and Crépey (2017) and Armenti and Crépey (2017) for applications in respective bilateral and centrally cleared trading setups. For other XVA frameworks, see for instance Brigo and Pallavicini (2014) or Bichuch, Capponi, and Sturm (2017) (without KVA) or, with a KVA meant as an additional contra-asset like the CVA and the FVA (as opposed to a risk premium in our case), Green (2015), Green, Kenyon, and Dennis (2014), or Elouerkhaoui (2016).…”

Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models

“…The hedger may also be requested to post additional cash collateral to the broker and, in some cases, he may be paid interest on his margin account with the broker. 1 To represent these trading arrangements for the ith risky asset, we set ψ i,l t = 0, α i t = α i+d t = 0 and…”

“…Let us only mention that most of these papers deal with linear markets with credit risk (possibly also with differential funding rates), whereas the general theory developed in this work aims to address problems where the emphasis is put on a nonlinear character of valuation in markets with imperfections. In contrast, Albanese et al [1], Albanese and Crépey [2], and Crépey et al [20] propose to address the issue of valuation adjustments through an alternative approach, which is based on the global valuation paradigm referencing to the balance sheet of the bank, its internal structure, and long-term interests of bank's shareholders. The issue of nonlinearity of trading does not appear in their approach, since the classical hedging arguments are no longer employed to determine the value of a new contract, which is added to the existing portfolio of bank's assets.…”