VEDANI Julien

In this paper we address some of the stability issues raised by the European life insurance regulation valuation scheme. Via an in-depth study of the so-called economic valuation framework, shaped through the market-consistency contract we first point out the practical interest of one of the El Karoui, Loisel, Prigent & Vedani (2017) propositions to enforce the stability of the cutoff dates used as inputs to calibrate actuarial models. This led us to delegitimize the argument of the no-arbitrage opportunity as a regulatory criteria to frame the valuation, and as an opposition to the previously presented approach. Then we display tools to improve the convergence of the economic value estimations be it the V IF or the SCR, using usual variance reduction methods and a specific work on the simulation seeds. Through various implementations on a specific portfolio and valuation model we decrease the variance of the estimators by over 16 times.

Presentation of an article published in the European Actuarial Journal in 2017 and the update of its results: EL KAROUI, Nicole, LOISEL, Stéphane, PRIGENT Jean-Luc and VEDANI, Julien.

The Solvency II directive has introduced a specific so-called risk-neutral framework to valuate economic accounting quantities throughout European life insurance companies. The adaptation of this theoretical notion for regulatory purposes requires the addition of a specific criterion, namely the market-consistency, in order to objectify the choice of the valuation probability measure. This paper aims at pointing out and fixing some of the major risk sources embedded in the current regulatory life insurance valuation scheme. We compare actuarial and financial valuation schemes. We then address first operational issues and potential market manipulation sources in life insurance, induced by both theoretical and regulatory pitfalls. For example, we show that calibrating the interest rate model in October 2014 instead of December 31 st 2014 generates a 140%-increase in the economic own funds of a representative French life insurance company. We propose various adaptations of the current implementations, including product-specific valuation scheme, to limit the impact of these market-inconsistencies.

The Solvency II directive has introduced a specific so-called risk-neutral framework to valuate economic accounting quantities throughout European life insurance companies. The adaptation of this theoretical notion for regulatory purposes requires the addition of a specific criterion, namely the market-consistency, in order to objectify the choice of the valuation probability measure. This paper aims at pointing out and fixing some of the major risk sources embedded in the current regulatory life insurance valuation scheme. We compare actuarial and financial valuation schemes. We then address first operational issues and potential market manipulation sources in life insurance, induced by both theoretical and regulatory pitfalls. For example, we show that calibrating the interest rate model in October 2014 instead of December 31 st 2014 generates a 140%-increase in the economic own funds of a representative French life insurance company. We propose various adaptations of the current implementations, including product-specific valuation scheme, to limit the impact of these market-inconsistencies.

The Solvency II Directive, submitted by the European Commission in 2009, came into force in January 2016. It is based on three pillars. The first pillar deals with quantitative requirements related to the calculation of the Solvency Capital Requirement. The second pillar deals with risk governance. The third pillar deals with required documents and information, market discipline. For life insurance, the quantitative requirements (Pillar I and part of Pillar II) introduce a high level of complexity. Indeed, in order to create a system adapted to the specificities of companies, the directive has introduced a framework for the valuation of the balance sheet of insurers that is very delicate to understand and use, the economic valuation. Because of this complexity, most European life insurers have, during their first years of implementing the directive, chosen to focus on pillar I knowing that the calculation of the capital requirement would be an essential part of the system. In this thesis, I have chosen to focus my work on the second pillar of the directive and more precisely on the Own Risk and Solvency Assessment (ORSA) process. This regulatory tool is in fact the second major source of complexity in Solvency II. It is a risk management process totally integrated in the company whose objective is to lead insurers to a better understanding of their risks. During my work, I tried to conceptualize and to propose operational implementations to answer the problems induced by the ORSA (calculation of the Global Solvency Requirement and Permanent Compliance). Finally, through a joint work with N. El Karoui, S. Loisel and J.-L. Prigent, we analyzed and exemplified some of the major dangers induced by economic valuation.

The Solvency II Directive, submitted by the European Commission in 2009, came into force in January 2016. It is based on three pillars. The first pillar deals with quantitative requirements related to the calculation of the Solvency Capital Requirement. The second pillar deals with risk governance. The third pillar deals with required documents and information, market discipline. For life insurance, the quantitative requirements (Pillar I and part of Pillar II) introduce a high level of complexity. Indeed, in order to create a system adapted to the specificities of companies, the directive has introduced a framework for the valuation of the balance sheet of insurers that is very delicate to understand and use, the economic valuation. Because of this complexity, most European life insurers have, during their first years of implementing the directive, chosen to focus on pillar I knowing that the calculation of the capital requirement would be an essential part of the system. In this thesis, I have chosen to focus my work on the second pillar of the directive and more precisely on the Own Risk and Solvency Assessment (ORSA) process. This regulatory tool is in fact the second major source of complexity in Solvency II. It is a risk management process totally integrated in the company whose objective is to lead insurers to a better understanding of their risks. During my work, I tried to conceptualize and to propose operational implementations to answer the problems induced by the ORSA (calculation of the Global Solvency Requirement and Permanent Compliance). Finally, through a joint work with N. El Karoui, S. Loisel and J.-L.

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.

Within the Own Risk and Solvency Assessment framework, the Solvency II directive introduces the need for insurance undertakings to have efficient tools enabling the companies to assess the continuous compliance with regulatory solvency requirements. Because of the great operational complexity resulting from each complete evaluation of the Solvency Ratio, this monitoring is often complicated to implement in practice. This issue is particularly important for life insurance companies due to the high complexity to project life insurance liabilities. It appears relevant in such a context to use parametric tools, such as Curve Fitting and Least Squares Monte Carlo in order to estimate, on a regular basis, the impact on the economic own funds and on the regulatory capital of the company of any change over time of its underlying risk factors. In this article, we first outline the principles of the continuous compliance requirement then we propose and implement a possible monitoring tool enabling to approximate the eligible elements and the regulatory capital over time. In a final section we compare the use of the Curve Fitting and the Least Squares Monte Carlo methodologies in a standard empirical finite sample framework, and stress adapted advices for future proxies users.