Nested Monte Carlo simulation in financial reporting: a review and a new hybrid approach

Risk assessment on a stochastic basis has become prevalent in financial reporting due to increasingly sophisticated regulatory requirements. Many applications require nested stochastic projections, for which crude Monte Carlo can be too costly and time-consuming to perform to reach a reasonable degree of accuracy. While there has been ample literature on nested simulation methods in the area of portfolio management, less is known in the literature regarding nested simulation for financial reporting and internal risk management. There has been little research dealing with unique challenges arising from the structure of insurance liabilities. This paper intends to fill the gap in the literature by providing an overview of the use of nested stochastic modeling for different regulatory purposes and investigating the multi-period nested stochastic model, common in insurance products. The paper reviews a variety of so-called 'stochastic-on-stochastic' methods to speed up nested simulations. In addition, the paper presents a new hybrid 'deterministic-on-stochastic' method based on partial differential equation (PDE). To the best knowledge of the authors, this is the first time that a PDE method has been introduced for the purpose of nested stochastic projection. A numerical example is provided to show the high efficiency of the hybrid PDE method in a multi-period nested model for financial reporting.