Reinterpretation of Solvency Capital Requirements Through an Analytical Formula

17 Pages Posted: 25 Nov 2011

See all articles by Ludovic Dubrana

Ludovic Dubrana

Ecole Nationale des Ponts et Chaussées (ENPC)

Date Written: November 1, 2011


In the context of Solvency II, insurance companies access and manage economic capital across various techniques requiring generally heavy Monte Carlo simulation procedures in order to derive an appropriate loss distribution. However, very little attention has been addressed to model Solvency Capital Requirements (SCR) based on the derivation of a closed-form formula. While the current industry standard is to make use of sophisticated algorithms requiring a significant calculation time given the current state-of-the-art computer technology and the amount of computational resources required for some techniques such as the stochastic-in-stochastic valuation that is particularly difficult to implement in practice for large participating Life insurance portfolios, a flexible and realistic modeling structure is proposed. This paper explores a convenient and straightforward solution for quantifying economic capital that aims at investigating notably the limited attempt that has been addressed so far at modeling economic capital via an adequate closed-form formula. The analytical formula proposed has the advantage of avoiding the use of simplified approaches such as the replicating portfolio for instance that has been largely criticized for its poor ability to replicate appropriately liabilities without introducing a significant error in the loss distribution covering against market risk. This paper contradicts the recent trend of highly complex modeling frameworks developed by some insurance companies for producing economic capital that can be hardly produced with high frequency and is in clear opposition with directives provided in CEIOPS. We aim to support the idea of developing a type of partial internal model allowing to better know the risks an insurance company is exposed to while keeping the attractive advantage of a closed-form solution. The approach adopted shows that SCR can be obtained based on the knowledge of systematic risks and conditional moments of order 1 and 2 of the distribution of net cash flows. An explicit solution for SCR is provided based on the derivation of a partial internal economic capital model that is general and flexible enough to further assess SCR via the inclusion of various assumptions largely detailed in this paper and allows to refine the approach. The attractive features of the modeling structure are its analytical formula, accuracy and encompass the interactions between assets and liabilities. Importantly, from our belief, the proposed modeling structure appears in accordance with CEIOPS, the general principles that aim to ensure a harmonized approach to the use of internal models throughout insurance companies.

Keywords: solvency capital requirements, SCR, solvency II, analytical formula, economic capital, partial internal model

JEL Classification: C00, C10, C13, C15, C40, C60, C61, C63, G00, G10, G11, G22

Suggested Citation

Dubrana, Ludovic, Reinterpretation of Solvency Capital Requirements Through an Analytical Formula (November 1, 2011). Available at SSRN: or

Ludovic Dubrana (Contact Author)

Ecole Nationale des Ponts et Chaussées (ENPC) ( email )

28, rue des Saints-Peres
75343 Paris Cedex 07

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