Abstract
In this work discuss the use of the standard model for the calculation of the solvency capital requirement (SCR) when the company aims to use the specific parameters of the model on the basis of the experience of its portfolio. In particular, this analysis focuses on the formula presented in the latest quantitative impact study (2010 CEIOPS) for non-life underwriting premium and reserve risk. One of the keys of the standard model for premium and reserves risk is the correlation matrix between lines of business. In this work we present how the correlation matrix between lines of business could be estimated from a quantitative perspective, as well as the possibility of using a credibility model for the estimation of the matrix of correlation between lines of business that merge qualitative and quantitative perspective.
Highlights
Parallel to the emergence of the earliest quantitative impact studies began a series of streams of discussion on the implementation of the Solvency II directive, and in general on the work of Committee of European Insurance and Occupational Pension's Supervisor (CEIOPS). Steffen (2008) highlighted the most marked aspects on Solvency II and CEIOPS work, and how the level of harmonization through the application of the principle of the three pillars between the different regulations of solvency in the European area should be increased
The standard formula[1] for this risk, and generally the standard model, can be used by entities using the parameters set for each line of business by the regulator as a proxy of market, or it can be adapted to the own risk profile through the estimation of new parameters based on the historical experience of the entity
Focusing on the pillar I of Solvency II, some authors have done some works on the estimation of the solvency capital requirement (SCR) of premium and reserves risk with the use of both proposals the standard and the internal model
Summary
In this paper we focus on the risk of inadequate premiums and reserves for nonlife business. The standard formula[1] for this risk, and generally the standard model, can be used by entities using the parameters set for each line of business by the regulator as a proxy of market, or it can be adapted to the own risk profile through the estimation of new parameters based on the historical experience of the entity. Another reason for the estimation of parameters could come determined from the fact that the business structure of an insurance company is not adapted to the lines of business proposed by the regulator, so it should estimate the parameters necessary to obtain the corresponding SCR adjusting to the own business model. On the last quantitative impact study (QIS) are presented various proposals for the estimation of specific standard deviations of premiums by line of business and standard deviations of reserves by lines of business. We discuss the methodology that could be used for the estimation of the correlations and what information would be relevant for these estimates
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