Deep xVA Solver – A Neural Network Based Counterparty Credit Risk Management Framework

Gnoatto, Alessandro; Picarelli, Athena; Reisinger, Christoph

doi:10.2139/ssrn.3594076

Cited by 21 publications

(9 citation statements)

References 54 publications

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“…We applied the scheme in some linear and non linear FBSDE examples and we found very good results even with a parsimonious number of quantization and time discretization points. This opens the door to more ambitious applications, like the computation of xVA on single and multiple positions, where our fully quantization based method can be used as a pricing tool in the learning phase of any Neural Network based counterparty credit risk algorithm, like the Deep xVA approaches of Gnoatto et al (2020) and Albanese et al (2020) and Abbas-Turki et al (2020).…”

Section: Discussionmentioning

confidence: 99%

A Fully Quantization-based Scheme for FBSDEs

Callegaro¹,

Gnoatto²,

Grasselli³

2021

Preprint

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We propose a quantization-based numerical scheme for a family of decoupled FBSDEs. We simplify the scheme for the control in Pagès and Sagna (2018) so that our approach is fully based on recursive marginal quantization and does not involve any Monte Carlo simulation for the computation of conditional expectations. We analyse in detail the numerical error of our scheme and we show through some examples the performance of the whole procedure, which proves to be very effective in view of financial applications.

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Section: Discussionmentioning

confidence: 99%

A Fully Quantization-based Scheme for FBSDEs

Callegaro¹,

Gnoatto²,

Grasselli³

2021

Preprint

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“…In this subsection, we show the accuracy of our algorithm. To this end, we compare our algorithm with the multi-FC DBSDE solver (E et al, 2017), whose validation for the valuation of defaultable claims has been examined by Gnoatto et al (2020). While the results obtained from multi-FC DBSDE serve as a benchmark, Table 5.2 demonstrates the ability of the single network-based algorithm in providing accurate numerical approximations even for dimension as high as 100.…”

Section: Comparison With the Multi-fc Dbsde Solver (E Et Al 2017)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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“…Lately, see for instance [21], deep learning techniques have been applied to evaluate a derivative depending on multiple risks, whose price is corrected by a family of adjustments that go under the acronym of XVA. This approach is based on the price characterization as solution of a Backward Stochastic Differential Equation and the application of machine learning to those equations.…”

Section: Introductionmentioning

confidence: 99%

CVA in fractional and rough volatility models

Alòs¹,

Antonelli²,

Ramponi³

et al. 2022

Preprint

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In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with the default event. We specialize it for some volatility models and we provide price approximations, based on the representation formula. We study numerically their accuracy, comparing the results with Monte Carlo simulations, and we run a theoretical study of the error. We also introduce a seminal study of roughness influence on the claim's price.

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Deep xVA Solver – A Neural Network Based Counterparty Credit Risk Management Framework

Cited by 21 publications

References 54 publications

A Fully Quantization-based Scheme for FBSDEs

A Fully Quantization-based Scheme for FBSDEs

Credit Valuation Adjustment with Replacement Closeout: Theory and Algorithms

CVA in fractional and rough volatility models

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