Structural properties of the NPV certainty equivalent of future flows.

Summary With the implementation of the Solvency II framework, insurers have the possibility to develop an internal model to better reflect the specificities of their own risks, rather than using a more simplified and less specific approach, the standard formula. In life insurance, the Simulations within Simulations (SoS) method is a first approach available to operational staff to evaluate the required solvency capital. This highly simulative approach provides a complete distribution of economic capital at one year, without the need for restrictive assumptions. However, its algorithmic complexity makes it operationally heavy to implement. The SoS gas pedal proposed by Devineau and Loisel (2008) reduces the number of simulations, using an a priori selection procedure of the most adverse scenarios. However, the selection is based on a given criterion, which, although relatively efficient, can be simplistic and appears optimistic. The Net Present Value of forward margins is a Net Present Value of margins calculated on a central scenario, in which all financial variables follow their expected trajectory. It provides information of a certain equivalent type regarding the expectation of the margin NPV, the economic equity. This article, which is a synthesis of an actuarial dissertation carried out by the authors, focuses on the properties of this Net Present Value of margins, known as forward, and on the means of using it in an operational framework to accelerate the simulatory approaches of economic capital calculation in life insurance.