Abstract
The definition of solvency for insurance companies, within the European Union, is currently being revised as part of Solvency II Directive. The new definition induces revolutionary changes in the logic of control and expands the responsibilities in business management. The rationale of the fundamental measures of the Directive cannot be understood without reference to probability distribution functions. Many insurers are struggling with the realisation of a so-called “internal model” to assess risks and determine the overall solvency needs, as requested by the Directive. The quantitative assessment of the solvency position of an insurer relies on Monte Carlo simulation, in particular on nested Monte Carlo simulation that produces very hard computational and technological problems to deal with. In this paper, we address methodological and computational issues of an “internal model” designing a tractable formulation of the very complex expectations resulting from the “market-consistent” valuation of fundamental measures, such as Technical Provisions, Solvency Capital Requirement and Probability Distribution Forecast, in the solvency assessment of life insurance companies. We illustrate the software and technological solutions adopted to integrate the Disar system—an asset–liability computational system for monitoring life insurance policies—in advanced computing environments, thus meeting the demand for high computing performance that makes feasible the calculation process of the solvency measures covered by the Directive.
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Notes
Whenever the term “market-consistent” valuation is referred in this paper, it is be construed as follows: if the contracts are hedgeable (and then market valuation is available) the market-consistent value is given by the market price, that is to say a “marked to market” valuation; if the contracts are non hedgeable (and then a market valuation is unavailable) the market consistency must be guaranteed by an evaluation model, that is to say a “marked to model” valuation.
The BE “shall correspond to the probability-weighted average of future cash-flows, taking account of the time value of money (expected present value of future cash-flows), using the relevant risk-free interest rate term structure, [...] up-to-date and credible information and realistic assumptions and be performed using adequate, applicable and relevant actuarial and statistical methods”; the RM “shall be such as to ensure that the value of the technical provisions is equivalent to the amount that insurance [...] undertakings would be expected to require in order to take over and meet [...] obligations” (Directive 2009, art. 77).
Otherwise, the risk margin is calculated using a “Cost-of-Capital” approach (Salzmann and Wüthrich 2010).
Here and in the following it is supposed that the RM for the non hedgeable risk components is zero.
The asset–liability management, in the Professional Actuarial Specialty Guide (Luckner et al. 2002), is defined as “the practice of managing a business so that decisions on assets and liabilities are coordinated; it can be defined as the ongoing process of formulating, implementing, monitoring and revising strategies related to assets and liabilities in an attempt to achieve financial objectives for a given set of risk tolerances and constraints”.
The extension to unit-linked and index-linked policies is straightforward in more usual cases.
At the end of year 2011 the Italian Supervisory Authority listed 386 segregated funds, belonging to 70 insurance companies, with the overall amount of statutory reserves summing up to about 305 billions euros.
A call option gives right to buy, whereas a put option means the right to sell, an asset—the underlying—at a predetermined price.
The methodological asset-liability management (ALM) framework in which DISAR has been designed is detailed in Castellani et al. (2004).
A more detailed description of the Disar system is given in Castellani and Passalacqua (2011).
See Table 1 in Castellani and Passalacqua (2011) for the list of main risk drivers with the corresponding model used in Disar for the valuation.
The first experiences of parallelization of the algorithm implemented in DiAlmEng are reported in Corsaro et al. (2009) presented to the 18th International AFIR Colloquium (2008). A complementary approach to the strategy described in Castellani and Passalacqua (2011) based on the parallelization of the simulations on multicore architecture has been developed in Corsaro et al. (2011) and De Angelis et al. (2013).
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Casarano, G., Castellani, G., Passalacqua, L. et al. Relevant applications of Monte Carlo simulation in Solvency II. Soft Comput 21, 1181–1192 (2017). https://doi.org/10.1007/s00500-015-1847-6
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DOI: https://doi.org/10.1007/s00500-015-1847-6