Sparse grid method for highly efficient computation of exposures for xVA
TLDR
In this article , the authors explore numerical techniques for improving the simulation of exposures, aiming to decimate the number of portfolio evaluations, particularly for large portfolios involving multiple, correlated risk factors.About:
This article is published in Applied Mathematics and Computation.The article was published on 2022-12-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Sparse grid & Computer science.read more
Citations
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Neural network expression rates and applications of the deep parametric PDE method in counterparty credit risk
Kathrin Glau,Linus Wunderlich +1 more
TL;DR: In this article , the authors provided the first approximation results, which feature a dimension-independent rate of convergence for deep neural networks with a hyperbolic tangent as the activation function, and confirmed that the deep parametric PDE method performs well in high-dimensional settings by presenting in a risk management problem of high interest for the financial industry.
Journal ArticleDOI
Accelerated Computations of Sensitivities for xVA
TL;DR: In this article , a polynomial approximation of the shocked and unshocked valuation functions is proposed for interest rate sensitivities of expected exposures, and the difference between these functions is approximated.
References
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High-Order Collocation Methods for Differential Equations with Random Inputs
Dongbin Xiu,Jan S. Hesthaven +1 more
TL;DR: A high-order stochastic collocation approach is proposed, which takes advantage of an assumption of smoothness of the solution in random space to achieve fast convergence and requires only repetitive runs of an existing deterministic solver, similar to Monte Carlo methods.
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High dimensional polynomial interpolation on sparse grids
TL;DR: The error bounds show that the polynomial interpolation on a d-dimensional cube, where d is large, is universal, i.e., almost optimal for many different function spaces.
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Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain
TL;DR: In this paper, the authors propose a more efficient implementation of the Smolyak method for interpolation, namely, they show how to avoid costly evaluations of repeated basis functions in the conventional SMolyak formula, and they extend the SMOLYAK method to include anisotropic constructions that allow to target higher quality of approximation in some dimensions than in others.
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On cross-currency models with stochastic volatility and correlated interest rates
TL;DR: In this paper, the authors construct multi-currency models with stochastic volatility and correlated interest rates with a full matrix of correlations and provide semi-closed form approximations which lead to efficient calibration.
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Chebyshev interpolation for parametric option pricing
TL;DR: The Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo and its combination with Monte Carlo simulation and the effect of (stochastic) approximations of the interpolation is analyzed.
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