Title: A sparse grid approach to balance sheet risk measurement,
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.