The capital requirements for insurance companies in the Solvency I framework are based on the premium and claim expenditure. This approach does not take the individual risk of the insurer into consideration and give policy holder little assur- ance. Therefore a framework called Solvency II is under development by EU and its members. The capital requirements in Solvency II are based on risk management and is related to the specific risks of the insurer. Moreover, the insurer must make disclosures both to the supervising authority and to the market. This puts pressure on the insurance companies to use better risk and capital management, which gives the policy holders better assurance. In this thesis we present a stochastic model that describes the development of assets and liabilities. We consider the following risks: Stock market, bond market, interest rate and mortality intensity. These risks are modeled by stochastic processes that are aggregated to describe the change in the insurers Risk Bearing Capital. The capital requirement, Solvency Capital Requirement, is calculated using Conditional Value-at-Risk at a 99% confidence level and Monte Carlo simulation. The results from this model is compared to the Swiss Solvency Test model for three different types of life insurance policies. We can conclude that for large portfolios, the model presented in this thesis gives a lower solvency capital requirement than the Swiss model for all three policies. For small portfolios, the capital requirement is larger due to the stochastic mortality risk which is not included in the Swiss model.

This thesis studies project Solvency II, which is focused on the integrated regulation of insurance market in the European Union. It presents basic division and capital requirements arising from it. It describes division of the project into the three areas, refered to as pillars in practice. The thesis summarizes the basic methods for measuring the risk (Value at Risk, Tail Value at Risk), necessary in the calculation of the solvency capital requirements. The thesis studies the method of calculation of the solvency capital requirement SCR and the minimum capital requirement MCR. The calculation of the SCR is focused mainly on the method of the calculation of the capital requirement using the standard formula. Lastly, capital requirements are calculated using concrete data set.

Title: Capital requirements imposed on insurance companies in Solveny II and their quantification Author: Bc. Martin Kožár Department: Department of probability and mathematical statistics Supervisor: Mgr. Martin Pleška Abstract: This thesis studies project Solvency II, which is focused on the integrated regulation of insurance market in the European Union. It pre- sents basic division and capital requirements arising from it. It describes division of the project into the three areas, refered to as pillars in practice. The thesis summarizes the basic methods for measuring the risk (Value at Risk, Tail Value at Risk), necessary in the calculation of the solvency capital requirements. The thesis studies the method of calculation of the solvency capital requirement SCR and the minimum capital requirement MCR. The calculation of the SCR is focused mainly on the method of the calculation of the capital requirement using the standard formula. Lastly, capital requi- rements are calculated using concrete data set. Keywords: Solvency II, solvency capital requirement SCR, minimum capital requirement MCR 1

We examine risk taking when the bank's preferences exhibit smooth ambiguity aversion. Ambiguity is modeled by a second-order probability distribution that captures the bank's uncertainty about which of the subjective beliefs govern the financial asset return risk. Ambiguity preferences are modeled by the (second-order) expectation of a concave transformation of the (first-order) expected utility of profit conditional on each plausible subjective distribution of the return risk. Within this framework, the banking firm finds it less attractive to take risk in the presence than in the absence of ambiguity. This result extends to the case of greater ambiguity aversion. Given that the competitive bank's smooth ambiguity preferences exhibit non-increasing absolute ambiguity aversion, imposing a more stringent capital requirement to the bank reduces the optimal amount of loans, if the bank's coefficient of relative risk aversion does not exceed unity. Ambiguity and ambiguity aversion as such have adverse effect on the bank's risk taking.

We specify a class of non-linear and non-Gaussian models for which we estimate and forecast the conditional distributions with daily frequency. We use these forecasts to calculate VaR measures for three different equity markets (US, GB and Japan). These forecasts are evaluated on the basis of different statistical performance measures as well as on the basis of their economic costs that go along with the forecasted capital requirements. The results indicate that different performance measures generate different rankings of the models even within one financial market. We also find that for the three markets the improvement in the forecast by non-linear models over linear ones is negligible, while non-gaussian models significantly dominate the gaussian models. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Sänkningen av aktiekapitalkravet från 100 000 till 50 000 SEK den 1 april 2010, förverkligades för att förbättra de institutionella villkoren för de privata aktiebolagen och för att fungera som ett incitament till att öka småföretagande. Syftet med denna uppsats är att undersöka om de privata aktiebolagen har valt att lösgöra eller behålla sitt aktiekapital efter denna nya regel och varför. Dessutom ämnar studien att undersöka om det finns skillnader mellan de som väljer att minska eller att behålla sitt aktiekapital avseende bransch, ålder och omsättning. Studien baseras på en enkätundersökning som innefattar 212 respondenter. De resultat som denna undersökning kommer fram till är:  Att majoriteten av de privata aktiebolagen har valt att behålla sitt aktiekapital. Att anledningen bakom att behålla aktiekapitalet är att bevara företagets kreditvärdighet, att använda aktiekapitalet i verksamheten och för att proceduren med att sänka aktiekapitalet anses vara krångligt och tidskrävande. Framförallt anser inte dessa företag att en minskning av aktiekapitalet har någon större betydelse då det mesta av minskningen antingen försvinner i form av beskattning eller att mängden 50 000 SEK inte anses vara en väsentlig summa. Skillnaderna mellan de privata aktiebolagen utgörs endast av omsättningsvolym. För företag med omsättning över 3 000 000 SEK/år tenderar en minskning av aktiekapitalet att avta helt och förkommer bland företagen med mindre omsättning än 3 000 000 SEK/år.  Detta innebär att de privata aktiebolagen som ingår i studien inte upplever möjligheten till att sänka aktiekapitalet som en förbättring av de institutionella villkoren eller som ett incitament, där regeln inte alls anses ha någon inverkan för företagen. / The reduction of share capital requirement from 100 000 to 50 000 SEK, which was implemented April 1, 2010 to improve the institutional conditions for the private limited companies and to act as an incentive to increase small businesses. The purpose of this essay is to examine whether the private limited companies have chosen to reduce or maintain its share capital after this new rule and why. In addition, the study intends to investigate whether there are differences between those who have chosen to reduce or maintain its share capital regarding branch, age and revenue. The study is based on a survey involving 212 respondents. The results of this study are the following: The majority of the private limited companies have chosen to maintain their share capital. The reason behind keeping the share capital is to maintain the company’s credit rating, to use the share capital in their respective the business and because of the process of lowering the share capital is considered to be complex and time consuming. Above all, these companies do not consider a reduction of share capital having a greater significance when most of the reduction either disappear in the form of taxation or the amount of 50 000 SEK is not considered as a substantial amount.  The differences among the private limited companies consist only of revenue. For companies with revenue of more than 3 000 000 SEK/year, tends a reduction of share capital to subside completely and occurs among the companies with turnover less than 3 000 000 SEK/year. This means that the private limited companies do not perceive the possibility of lowering the share capital as an improvement of the institutional conditions or as an incentive where the reduction of share capital requirement is not considered to have any impact on businesses.

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In this thesis we will deal with the term of operational risk, as it is presented in the directives Basel 2 that are mandatory for financial institutions in the European Union. The main problem is operational risk modeling, therefore, how to measure and manage it. In the first part we will look at the possibility of calculating the capital requirements for operational risk under Basel 2, mainly the calculation with the internal model. We will describe the specific procedures for the development of the internal model and we will focus on Loss Distribution Approach. The internal model will be based on modeling of loss in each risk cell separately. In the second part we will show, how to include modeling of dependence structure between risk cells to the internal model with using copulas. Finally, we will show the illustrative example, where we will see, whether the modeling of dependence leads to a reduction of the total capital requirement. Powered by TCPDF (www.tcpdf.org)

This thesis is focused on the new basel capital accord - Basel II. The first part of the work deals with financial risks and their regulation. Next part is concerned on Basel I and Basel II. This part defines basic terminology and three pillars - minimum capital requirements, supervisory review process and market discipline. In the last part there is an analysis of impact of Basel II on capital adequacy of czech banks.

The diploma thesis focuses on the topic of the future regulatory regime of the insurance and reinsurance market of the European Union called Solvency II. Currently the most discussed issue without a final structure is an extensive set of legislative and technical changes not only in the area of solvency treatment. Primarily, the work focuses on the standard formula calculation of capital requirements that reflect the solvency position of companies on the market. The first part deals with the theoretical description of the calculating methods of the required capital levels under current and future rules on the basis of available official documents. Further the general overview of the Solvency II is presented, a more detailed description of the valuation techniques of balance sheet items for the purposes of Solvency II, dealing with company's own funds and possible ways to optimize the asset portfolio are also included. Some theoretical descriptions of computational procedures applied on a fictitious life insurance company are presented in the second, more practical part of the diploma thesis.