Tools for testing the Solvency Capital Requirement for life insurance

Longevity risk is one of the major risks that an insurance company or a pension fund has to deal with and it is expected that its importance will grow in the near future. In agreement with these considerations, in Solvency II regulation the Standard formula furnished for calculating the Solvency Capital Requirement explicitly considers this kind of risk. According to the new European rules in our paper we suggest a multiperiod approach to evaluate the SCR for longevity risk. We propose a backtesting framework for measuring the consistency of SCR calculations for life insurance policies.

Managing marginal capital requirements in solvency II: Analysis of a real insurance portfolio

This thesis provides a complete analysis of the Standard Capital Requirements given by Solvency II for a real insurance portfolio. We analyze the investment portfolio of BPI Vida e Pensões, an insurance company affiliated with a Portuguese bank BPI, both at security, sub-portfolio and asset class levels. By using the Standard Formula from EIOPA, Total SCR amounts to 239M€. This value is mostly explained by Market and Default Risk whereas the former is driven by Spread and Concentration Risks. Following the methodology of Leblanc (2011), we examine the Marginal Contribution of an asset to the SCR which allows for the evaluation of the risks of each security given its characteristics and interactions in the portfolio. The top contributors to the SCR are Corporate Bonds and Term Deposits. By exploring further the composition of the portfolio, our results show that slight changes in allocation of Term and Cash Deposits have severe impacts on the total Concentration and Default Risks, respectively. Also, diversification effects are very relevant by representing savings of 122M€. Finally, Solvency II represents an opportunity for the portfolio optimization. By constructing efficient frontiers, we find that as the target expected return increases, a shift from Term Deposits/ Commercial Papers to Eurozone/Peripheral and finally Equities occurs.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Solvency Capital estimation and Risk Measures

This paper examines why a financial entity’s solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement -SCR-, under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Prediction of individual automobile RBNS claim reserves in the context of Solvency II

Automobile bodily injury (BI) claims remain unsettled for a long time after the accident. The estimation of an accurate reserve for Reported But Not Settled (RBNS) claims is therefore vital for insurers. In accordance with the recommendation included in the Solvency II project (CEIOPS, 2007) a statistical model is here implemented for RBNS reserve estimation. Lognormality on empirical compensation cost data is observed for different levels of BI severity. The individual claim provision is estimated by allocating the expected mean compensation for the predicted severity of the victim’s injury, for which the upper bound is also computed. The BI severity is predicted by means of a heteroscedastic multiple choice model, because empirical evidence has found that the variability in the latent severity of injured individuals travelling by car is not constant. It is shown that this methodology can improve the accuracy of RBNS reserve estimation at all stages, as compared to the subjective assessment that has traditionally been made by practitioners.

The role of auditors in the Finnish limited liability companies as to solvency test in the context of asset distribution

Suomen osakeyhtiölain mukaan varoja ei saa jakaa, jos jaosta päätettäessä tiedetään tai pitäisi tietää yhtiön olevan maksukyvytön tai jaon aiheuttavan maksukyvyttömyyden. Ongelmallista on, että maksukykyä ei ole selvästi määritelty laissa tai hallituksen esityksessä. Tilintarkastuslain mukaan tilintarkastajan on siten huomautettava, jos maksukykytestiä on rikottu, mutta tilintarkastaja joutuu yleensä määrittelemään tällaiset huomauttamista vaativat tilanteet itse. Maksukykytestistä on kirjoitettu suomalaisessa yhtiöoikeuden ja laskentatoimen kirjallisuudessa melko kattavasti. Kuitenkin tilintarkastajaa koskeva näkökulma on saanut osakseen suhteellisen vähän huomiota. Tästä näkökulmasta on kirjoitettu vain joitakin korkeakoulujen tutkielmia sekä lyhyehköjä ammatillisia seminaariesityksiä. Tämän tutkielman tavoitteena on ollut koota laaja yleiskuva siitä, miten tilintarkastajat itse kokevat asemansa ja tehtävänsä yllä kuvatuissa tilanteessa. Tutkielmassa on käyty läpi aikaisempaa yhtiöoikeuden ja laskentatoimen kirjallisuudessa ja seminaariesityksissä esitettyä aineistoa. Lisäksi tutkielmaa varten tehtiin suomalaisille tilintarkastajille kohdennettu Internet-pohjainen kysely. Tutkielma selkeyttää kuvaa siitä, miten tilintarkastajat toimivat yllä kuvatussa tilanteessa ja miten he ovat sopeuttaneet toimiaan yhteiskunnan institutionaalisen asetelman muututtua. Kirjallisuuden pohjalta tapahtuva teoreettinen analyysi on yhdistetty kyselyyn siitä, miten tilintarkastajat käytännössä toimivat. Tutkimuksen perustana olevaa tietoa on analysoitu pääosin kyselytutkimuksen menetelmin, mutta myös tilastollisen tutkimuksen menetelmiä on käytetty. Tutkielman tuloksena tutkielmassa selvitetään tilintarkastajan tehtäviä maksukykytestin yhteydessä. Tuloksena voidaan myös todeta, että tilintarkastaja ei suorita varojenjaossa tarvittavan maksukyvyn arvioinnin kannalta keskeisiä tarkastustoimenpiteitä ainoastaan tilikauden päättymisen jälkeen. Päinvastoin, tällaisia tarkastustoimenpiteitä suoritetaan enemmän tai vähemmän koko tilintarkastuksen aikana. Lisäksi vaikuttaisi siltä, että tilintarkastajan oma suhtautuminen maksukykytestiin on ainakin jossain määrin merkityksellinen sen kannalta, kuinka paljon tarkastustoimenpiteitä tehdään ja kuinka paljon maksukyvystä ja siihen liittyvistä puutteista raportoidaan yhtiön johdolle.

Countercyclical regulation in Solvency II: merits and flaws. CEPS Commentary, 25 June 2012

October 2011 saw the latest draft of Solvency II, the European Union’s code for regulation of the insurance industry. This commentary, a collective effort by a group of academics specializing in financial, banking and insurance institutions, argues that the latest proposals need to be drafted again, urgently.