Geodesic
A sparse grid approach to balance sheet risk measurement
Cyril Bénézet1 ; Jérémie Bonnefoy2 ; Jean-François Chassagneux1 ; Shuoqing Deng3 ; Camilo Garcia Trillos4 ; Lionel Lenôtre5
1 Paris Diderot University, LPSM
2 Group Risk Management, GIE AXA
3 Paris Dauphine University, CEREMADE
4 University College London
5 Ecole Polytechnique, CMAP
ESAIM. Proceedings, Tome 65 (2019), pp. 236-265.

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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.
DOI : 10.1051/proc/201965236

Cyril Bénézet 1 ; Jérémie Bonnefoy 2 ; Jean-François Chassagneux 1 ; Shuoqing Deng 3 ; Camilo Garcia Trillos 4 ; Lionel Lenôtre 5

1 Paris Diderot University, LPSM
2 Group Risk Management, GIE AXA
3 Paris Dauphine University, CEREMADE
4 University College London
5 Ecole Polytechnique, CMAP 
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     author = {Cyril B\'en\'ezet and J\'er\'emie Bonnefoy and Jean-Fran\c{c}ois Chassagneux and Shuoqing Deng and Camilo Garcia Trillos and Lionel Len\^otre},
     title = {A sparse grid approach to balance sheet risk measurement},
     journal = {ESAIM. Proceedings},
     pages = {236--265},
     publisher = {mathdoc},
     volume = {65},
     year = {2019},
     doi = {10.1051/proc/201965236},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965236/}
}
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%A Jean-François Chassagneux
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%A Lionel Lenôtre
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Cyril Bénézet; Jérémie Bonnefoy; Jean-François Chassagneux; Shuoqing Deng; Camilo Garcia Trillos; Lionel Lenôtre. A sparse grid approach to balance sheet risk measurement. ESAIM. Proceedings, Tome 65 (2019), pp. 236-265. doi : 10.1051/proc/201965236. http://geodesic.mathdoc.fr/articles/10.1051/proc/201965236/

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