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Solvency II Methods for Life Insurance
Benešová, Martina ; Finfrle, Pavel (advisor) ; Mazurová, Lucie (referee)
Název práce: Metodiky Solvency II v životním pojištění Autor: Martina Benešová Katedra (ústav): Katedra pravděpodobnosti a matematické statistiky Vedoucí bakalářské práce: RNDr. Pavel Finfrle, Ph.D e-mail vedoucího: finfrle@generalippf.eu Abstrakt: Tato diplomová práce se zabývá problematikou solventnosti pojišťoven v souvislosti s konceptem regulatorního rámce Solvency II. Na začátku práce jsou shrnuté základní body o Solvency I, dále je větší pozornost věnovaná vlastnostem Solvency II a jednotlivým kategoriím rizik, jejichž správná kvantifikace je pro Solvency II klíčová. V další části jsou představeny metody na výpočet kapitálové dostatečnosti - interní a částečné interní modely a podrobněji pak standardní model. Klíčové dvě kapitoly práce se pak detailně zabývají rizikem storen v ži- votním pojištění. Rozebrána je standardní metodika výpočtu kapitálového poža- davku, a je navržen stochastický model, který ji rozšiřuje zahrnutím informace o diverzitě odbytových cest. Monte Carlo simulací je demonstrována nižší rizikovost pojišťovny s širším polem zprostředkovatelů. Klíčová slova: solventnost, Solvency II, kapitálové požadavky, riziko storen Title: The methods of Solvency II for life insurance Author: Martina Benešová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Pavel...
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Technical reserves of non-life insurance in the internal solvency models
Thomayer, Jiří ; Mertl, Jakub (advisor) ; Pešta, Michal (referee)
Title: Technical reserves of non-life insurance in the internal solvency model Author: Bc. Jiří Thomayer Department: Department of Propability and Mathematical Statistics Supervisor: Mgr. Ing. Jakub Mertl Abstract: In this work we study and describe calculation of solvency capital using the standard formula contained in the Directive of the European Union (Solvency II), which should be put into practice in Europe on 1 January 2013. This calcu- lation is described in quantitative impact study 5. We describe a general approach to risk measurement and we show some particular practical measures used to risk measurement. We explain under what conditions the standard formula or its parts can be replaced by internal model. Next, we show disadvantages of using the stan- dard formula and we propose possible internal model to calculate risk premiums and risk reserves in non-life insurance. Finally we apply the proposed model for calculation risk reverses in non-life insurance in practice. Keywords: Standard formula, Risk measurement, Solvency II, Internal model;
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Solvency Internal models
Mertl, Jakub ; Cipra, Tomáš (advisor) ; Mazurová, Lucie (referee) ; Jedlička, Petr (referee)
Title: Solvency Internal models Author: Mgr. Ing. Jakub Mertl Abstract: The subject of thesis is assessment of calculation methods on capital adequacy of currently implemented regulation in insurance industry called Solvency II. The aim of the thesis is to build up a partial internal model fulfilling the condition of Solvency II. The thesis deals with the premium and reserve risks that are essential part of non-life business. Different approaches of risk assessment are described and aggregation of those risks as well. An important part of the thesis is a numerical example illustrating presented methods.
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The economic capital and the price of risk in a pension fund
Čupák, Matúš ; Finfrle, Pavel (advisor) ; Mandl, Petr (referee)
In the present work we study the economic capital of pension funds and their possible extension into the new concept of Solvency II. The main task is to examine the risks that are characteristic for pension fund activity. We use several modified stress simulations, which we model using a virtual model of pension fund. Primarily we focus on changes in net asset value (NAV) which is used in standard formula for calculation of the solvency capital requirement (SCR). In conclusion, we evaluate the possible impact of applications Solvency II to pension funds, the resulting economic capital and solvency of modeled pension fund.
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Non-proportional Reinsurance in Solvency II
Havlíková, Tereza ; Justová, Iva (advisor) ; Mazurová, Lucie (referee)
Title: Non-proportional Reinsurance in Solvency II Author: Tereza Havlíková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Iva Justová, Ph.D. Supervisor's e-mail address: iva justova@hotmail.com Abstract: The aim of this thesis is to analyse non-proportional reinsurance of non-life insurance. Taking into account the latest Quantitative Impact Study QIS 5, we calculate the capital requirement under Solvency II and we focus on the premium and reserve risk. The first part of this work describes basic concepts and formulas. Furthermore, in the main part we describe the standard formula for the calculation of the capital requirement from which we derive a formula for the calculation of the capital requirement but this time taking into account the impact of reinsurance. In the last chapter, we apply the approach on an example, in which we examine the influence of parameters on the capital requirement. Keywords: non-proportional reinsurance, Solvency II, non-life underwriting risk 1
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Interest rate spreads on government bonds
Antoniewiczová, Petronella ; Žák, Kamil (advisor) ; Hurt, Jan (referee)
This work deals with the breakdown of government bonds yields on the risk components. More specifically it deals with cost of liquidity capital, loss of illiquidity and expected default losses. In the beginning we explain the characteristics of bonds, particularly government bonds, further we deal with some of elements which may break up the government bonds yields. Finally, we implement the interest rates of bonds of three EU member states and we will illustrate on Vasicek's model how to imitate part of risk free interest
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Capital requirements for insurance companies under Solvency II and its quantification
Kožár, Martin ; Pleška, Martin (advisor) ; Mazurová, Lucie (referee)
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
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Non-life Underwriting Risk in Solvency II - Undertaking Specific Parameters
Šimková, Barbora ; Justová, Iva (advisor) ; Mazurová, Lucie (referee)
of the bachelor's thesis Title: Non-life Underwriting Risk in Solvency II - Undertaking Specific Parameters Author: Barbora Šimková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Ing. Iva Justová Ph.D. Abstract: The thesis deals with methods by which it is possible to calculate specific estimate of standard deviation of risk in non-life premium risk. Premium risk is the risk caused by lack of insurance, when the undertaking does not have sufficient cover for future losses. Calculation methods are based on static methods and they comprise the knowledge taught at MFF UK. The thesis analyzes methods of calculating specific parameters and it explains how to calculate capital requirement for non-life premium and reserve risk; capital requirement reflects parameters of risk. An assessment of cap- ital requirements that uses specific parameters for an undertaking is in conclusion of the thesis. The evaluation is performed on a group of insurance companies from dif- ferent countries that used replacement of specific parameters in the calculation of risk premiums in Solvency II. Keywords: non-life underwriting risk, Solvency II, undertaking specific parameters
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Credit risk
Srbová, Eliška ; Herman, Jiří (advisor) ; Hurt, Jan (referee)
This thesis deals with credit risk and selected methods of its evalua- tion. It is focused on assumptions, calculation methods, results and specifics of the CreditMetrics and the CreditRisk+ models. The CreditRisk+ model analytically determines the portfolio credit losses distribution that is caused by defaults of counterparties. In the CreditMetrics model, the credit migration risk is addition- ally considered and the future portfolio value distribution is calculated using the Monte Carlo simulation. The third approach covered in this thesis is the Solvency II, the set of requirements proposed by the European Union for determination of regulatory capital for insurance companies. In the practical part the three ap- proaches are applied on a set of three portfolios of different credit quality. Their results, particularly the determined level of capital required to cover the risk of unexpected credit losses, are analyzed and compared.
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