Pricing of Counterparty Risk and Funding With CSA Discounting, Portfolio Effects and Initial Margin

Biagini, Francesca; Gnoatto, Alessandro; Oliva, Immacolata

doi:10.2139/ssrn.3394928

Cited by 5 publications

(5 citation statements)

References 46 publications

(66 reference statements)

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“…(2.8) Observe that the system (2.3) and (2.8) is decoupled, in the sense that the forward equation (2.3) does not exhibit a dependence on the backward component. We follow here the framework in Biagini et al (2019), where the portfolio dynamics are stated in the form of a BSDE under the enlarged filtration G. We set…”

Section: M and Set āMmentioning

confidence: 99%

“…where Vt := M m=1 V m t and R B , R C are two positive constants representing the recovery rate of the bank and the counterparty, respectively. In their Theorem 3.15, Biagini et al (2019) show that there exists a unique solution (V, Z, U ) for the G-BSDE (2.10), and the process V assumes the following form on {τ > t}:…”

Section: M and Set āMmentioning

confidence: 99%

“…To prove existence and uniquencess for the G-BSDE, Biagini et al (2019) employ the technique introduced by Crépey (2015a) and reformulate the problem under the reduced filtration F. Stated in such a form, the problem is also more amenable to numerical computations, especially in the case where f and θ do not dependent on V , either explicitly, or implicitly through C. We consider the following F-BSDE on [0, T ]:…”

Section: M and Set āMmentioning

confidence: 99%

See 2 more Smart Citations

Deep xVA solver -- A neural network based counterparty credit risk management framework

Gnoatto¹,

Picarelli²,

Reisinger³

2020

Preprint

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In this paper, we present a novel computational framework for portfolio-wide risk management problems where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method utilises a coupled system of BSDEs for the valuation adjustments (xVA) and solves these by a recursive application of a neural network based BSDE solver. This not only makes the computation of xVA for high-dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xVA, and allows simulations of the collateral account.

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Section: M and Set āMmentioning

confidence: 99%

Section: M and Set āMmentioning

confidence: 99%

Section: M and Set āMmentioning

confidence: 99%

See 1 more Smart Citation

Deep xVA solver -- A neural network based counterparty credit risk management framework

Gnoatto¹,

Picarelli²,

Reisinger³

2020

Preprint

Self Cite

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show abstract

“…Cesari et al (2009), Green (2015), Lichters et al (2015) and Sokol (2014), the market standard for xVA involves the computation of valuation adjustment at the level of the full portfolio as a way to capture the beneficial effect of netting agreements and this in turn implies the need to construct high dimensional Monte Carlo simulation models simultaneously covering all risk factors in all currencies relevant for the portfolio between the hedger and the counterparty. For a discussion of the subtleties in the computation of valuation adjustments in the presence of netting agreements we refer the reader to Biagini et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Cross Currency Valuation and Hedging in the Multiple Curve Framework

Gnoatto

Seiffert²

2020

SSRN Journal

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We generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Pallavicini (2017), andFujii et al. (2010b).In doing this, we provide a complete study of absence of arbitrage in a multi-currency market where, in each single monetary area, multiple interest rates coexist. We first characterize absence of arbitrage in the case without collateral.After that we study collateralization schemes in a very general situation: the cash flows of the contingent claim and those associated to the collateral agreement can be specified in any currency. We study both segregation and rehypothecation and allow for cash and risky collateral in arbitrary currency specifications. Absence of arbitrage and pricing in the presence of collateral are discussed under all possible combinations of conventions.Our work provides a reference for the analysis of wealth dynamics, we also provide valuation formulas that are a useful foundation for cross-currency curve construction techniques. Our framework provides also a solid foundation for the construction of multi-currency simulation models for the generation of exposure profiles in the context of xVA calculations.2010 Mathematics Subject Classification. 91G30, 91B24, 91B70. JEL Classification E43, G12.

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“…See for exampleJarrow and Yu (2001),Blanchet-Scalliet and Jeanblanc (2004) Bielecki et al (2008),Brigo and Chourdakis (2009a) andBrigo and Chourdakis (2009b) for the valuation of defaultable financial claims under the risk-free closeout convention.2 See Chapter CAP50 of Basel III.3 Quoting from ISDA (2010): "Upon default close-out, valuations will in many circumstances reflect the replacement cost of transactions calculated at the terminating party's bid or offer side of the market, and will often take into account the creditworthiness of the terminating party. "4 See for exampleCrépey et al (2010),Hu et al (2012), Henry-Labordère (2012),Brigo et al (2016) andBiagini et al (2019).…”

mentioning

confidence: 99%

Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms

Sun¹,

Tan²,

Wei³

2022

Preprint

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The replacement closeout convention has drawn more and more attention since the 2008 financial crisis. Compared with the conventional risk-free closeout, the replacement closeout convention incorporates the creditworthiness of the counterparty and thus providing a more accurate estimate of the Mark-to-market value of a financial claim. In contrast to the risk-free closeout, the replacement closeout renders a nonlinear valuation system, which constitutes the major difficulty in the valuation of the counterparty credit risk.In this paper, we show how to address the nonlinearity attributed to the replacement closeout in the theoretical and computational analysis. In the theoretical part, we prove the unique solvability of the nonlinear valuation system and study the impact of the replacement closeout on the credit valuation adjustment. In the computational part, we propose a neural network-based algorithm for solving the (high dimensional) nonlinear valuation system and effectively alleviating the curse of dimensionality. We numerically compare the computational cost for the valuations with risk-free and replacement closeouts. The numerical tests confirm both the accuracy and the computational efficiency of our proposed algorithm for the valuation of the replacement closeout.

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Pricing of Counterparty Risk and Funding With CSA Discounting, Portfolio Effects and Initial Margin

Cited by 5 publications

References 46 publications

Deep xVA solver -- A neural network based counterparty credit risk management framework

Deep xVA solver -- A neural network based counterparty credit risk management framework

Cross Currency Valuation and Hedging in the Multiple Curve Framework

Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms

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