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 & 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.
Highlights
The goal of this paper is to present a robust and efficient method to numerically assess risks on the balance sheet distribution of, say, an insurance company, at a given horizon
On the Liability side, the insurance company has sold a structured financial product which depends on the evolution of a one-dimensional stock price (St) and the risk-free interest rate
For a spectral risk measure, the two approaches give an estimation of (η) which converges to the true value, see Theorem 3.8
Summary
The goal of this paper is to present a robust and efficient method to numerically assess risks on the balance sheet distribution of, say, an insurance company, at a given horizon. Last, this permits to numerically quantify uncertainty.
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