A sparse grid approach to balance sheet risk measurement

Cyril Bénézet (cyril.benezet@polytechnique.edu), Jérémie Bonnefoy, Jean-François Chassagneux (chassagneux@ensae.fr), Shuoqing Deng, Camilo Garcia Trillos and Lionel Lenotre (lionel.lenotre@uha.fr)
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Lionel Lenotre: IRIMAS - Institut de Recherche en Informatique Mathématiques Automatique Signal - IRIMAS - UR 7499 - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar

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Abstract: 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 & Scholes 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.

Date: 2017-07-17
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Published in CEMRACS 2017 - Numerical methods for stochastic models : control, uncertainty quantification, mean-field, Jul 2017, Marseille, France. pp.236-265, ⟨10.1051/proc/201965236⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04133423

DOI: 10.1051/proc/201965236

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