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

Abstract

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.

Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning

“…The progress reviewed here has opened up a host of new possibilities, both in theory and applications. In applications, it has been proved effective in finance, such as the pricing of financial derivatives [11][12][13]154] and credit valuation adjustment [64]. It also opens up new possibilities in control theory, an area that has long been hindered by the CoD problem.…”

“…One can take the usual neural network models to represent the trial function. In high dimensions one needs an effective Monte Carlo algorithm to discretize the integral in (64). The interplay between the discretisation of the integral and the discretisation of the trial function using neural network models is an interesting issue that requires further attention.…”

“…The interplay between the discretisation of the integral and the discretisation of the trial function using neural network models is an interesting issue that requires further attention. Finally, SGD can be used naturally, similar to the situation in deep BSDE: the integral in the functional (64) plays the role of the expectation in deep BSDE. One notable issue is the choice of the activation function.…”

Neural networks-based algorithms for stochastic control and PDEs in finance

“…A close method introduced by [Rai18] uses also a single neural network U(t, x) : [0, T ]×R d → R and estimates Z as the automatic derivative in space of U. We also refer to [JO19] for a variation of this deep BSDE scheme to curve-dependent PDEs arising in the pricing under rough volatility model, to [GPR20] for a development of deep BSDE method to XVA solver, to [NR19] for approximations methods for Hamilton-Jacobi-Bellman PDEs, to [KSS20] for extension of deep BSDE scheme to elliptic PDEs with applications in insurance, and to [Ji+20] for the resolution of PDEs associated to fully coupled forward-backward SDEs.…”

Diseño de un modelo de gestión del riesgo de crédito en la red de agentes de empresas de servicios posventa Utilización de los componentes financieros de los servicios posventa y algoritmos meta innovadores

“…However, the truth is that when this default occurs, it often causes a lot of damage to the loan It becomes lenders or creditors, but we don't know how to measure the amount of these losses in advance to take the approach of different authors about this issue is different and clear Ace to Use in this way also in the same way (Giudici et al, 2021;Gnoatto et al, 2020).…”