Volume 65, 2019CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|236 - 265
|02 April 2019
A sparse grid approach to balance sheet risk measurement
Paris Diderot University, LPSM
2 Group Risk Management, GIE AXA
3 Paris Dauphine University, CEREMADE
4 University College London
5 Ecole Polytechnique, CMAP
In this work, we present a numerical method based on a sparse grid approximation to compute the loss distribution of the balance sheet of a financial or an insurance company. We first describe, in a stylised way, the assets and liabilities dynamics that are used for the numerical estimation of the balance sheet distribution. For the pricing and hedging model, we chose a classical Black & choles model with a stochastic interest rate following a Hull & White model. The risk management model describing the evolution of the parameters of the pricing and hedging model is a Gaussian model. The new numerical method is compared with the traditional nested simulation approach. We review the convergence of both methods to estimate the risk indicators under consideration. Finally, we provide numerical results showing that the sparse grid approach is extremely competitive for models with moderate dimension.
© EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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