Ve světě plném rizik má své nezastupitelné místo pojišťovna, která obchoduje s pojistným rizikem. V rámci své hospodářské činnosti na sebe přebírá, oceňuje, řídí a diverzifikuje rizika ostatních ekonomických subjektů. V zájmu ochrany vynaložených finančních prostředků na pojistnou ochranu a důvěry ekonomických subjektů podléhá pojišťovna regulaci ze strany státního dozoru, kdy jedna z důležitých činností je sledování její solventnosti. Současná metodika solventnosti neodráží dostatečně situaci měnícícho se tržního prostředí, a proto se pracuje na nové metodice pod názvem Solvency II.

This thesis is primarily focused on forthcoming regulatory concept Solvency II, which is valid for all member states of the European Union in insurance industry. In the first part of the work the term solvency is defined and actual mode of its reporting called Solvency I with its basic shortcomings are introduced. The second part describes the forthcoming new concept called Solvency II, its aims, three pillars on which it stands on and also the Lamfalussy Legislative Model according to which it is created. Then the fundamental risks endangering the insurance companies and the timetable of the Solvency II implementation are explained. The analysis of five Quantitative Impact Studies focused on impacts of the Solvency II concept makes the finish of the work.

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.

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.

Throughout Europe, the introduction of Solvency II is forcing companies in the life assurance and pensions provision markets to change how they estimate their liabilities. Historically, each solvency assessment required that the estimation of liabilities was performed once, using actuaries' views of economic and demographic trends. Solvency II requires that each assessment of solvency implies a 1-in-200 chance of not being able to meet the liabilities. The underlying stochastic nature of these requirements has introduced significant challenges if the required calculations are to be performed correctly, without resorting to excessive approximations, within practical timescales. Currently, practitioners within UK pension provision companies consider the calculations required to meet new regulations to be outside the realms of anything which is achievable. This project brings the calculations within reach: this thesis shows that it is possible to perform the required calculations in manageable time scales, using entirely reasonable quantities of hardware. This is achieved through the use of several techniques: firstly, a new algorithm has been developed which reduces the computational complexity of the reserving algorithm from O(T2) to O(T) for T projection steps, and is sufficiently general to be applicable to a wide range of non unit-linked policies; secondly, efficient ab-initio code, which may be tuned to optimise its performance on many current architectures, has been written; thirdly, approximations which do not change the result by a significant amount have been introduced; and, finally, high performance computers have been used to run the code. This project demonstrates that the calculations can be completed in under three minutes when using 12,000 cores of a supercomputer, or in under eight hours when using 80 cores of a moderately sized cluster.

The Diploma thesis deals with the risk management in an insurance company. The main goal of the thesis is to determine the process of the risk management in insurance companies and to compare this process with the theory and with requirements of directive Solvency II. The first part of the thesis specifies the issue from a theoretical view. The second part focuses on a real situation in insurance companies and concrete approaches of quantitative assessment of risks, such a Value at Risk and stress testing. The result of the thesis is the evaluation of readiness of insurance companies for implementation of directive Solvency II and recommendations for an improvement of the process of risk management.

The Diploma thesis deals with the analysis of current approaches to the creation and a financial placement of technical provisions. The first part defines the technical provisions and their creation with regard to the application of Solvency II. The thesis also deals with the principles and structure of financial placement. Due to a past financial crisis that affected not only banks, but also insurance companies, the thesis will also focus on the relationship of the financial crisis on investment of technical provisions. In the second part the thesis describes the approach and creation of technical provisions and financial placements of specific commercial insurance companies and its comparison with other insurance companies. The result of the thesis is the evaluation and recommendations for optimization of technical provisions and financial investment for the insurance companies.

The Master thesis deals with solvency testing of commercial insurance companies using 3 different solvency systems - Solvency II, Swiss Solvency Test and the Canadian system of solvency testing. Each method of solvency testing is analysed within each solvency system. After deducting the strong and weak points of each system, there are proposals made for the most convenient and optimal system of solvency testing with regard to all specific attributes of insurance market.

The three chapters all address solvency regulation issues, with a focus on market risks under the Solvency II framework. Chapter 1 deals with “high-level” aspects of Solvency II as main principles and the general structure. Chapters 2 and 3 will be devoted to quantitative issues. Chapter 1 describes the main evolutions that led to the development of Solvency II. The insurance sector has dramatically evolved during the last two decades. Among others developments, we stress the new risks faced by the sector as natural catastrophes, changing demographics or market risks. Insurers become international companies, investing almost 10 trillion € of assets in Europe at the end of 2014 and being increasingly intertwined with banks and other financial sectors. Financial innovation and the refinement of risk management techniques and models developed by companies have gained momentum among the major European insurance companies. Have these evolutions changed the needs for the supervisory of insurance companies? The economic foundation for regulation is based on the presence of market failures, including severe asymmetric information problems and principal-agent conflicts. Insurance consumers, particularly individuals and households, face significant challenges in judging the financial risk of insurers. But the importance of the insurance sector for financial stability has been increasing. A sound regulatory and supervisory system is necessary to maintain efficient, safe, fair and stable financial markets and promote growth and competition in the insurance sector. The difficult conditions experienced by the industry and the shortcomings of the previous regulatory and supervisory framework have forced regulators to take action to change the way in which they regulate insurance companies’ solvency. Recognizing the shortcomings of Solvency I, EU policy-makers undertook the Solvency II project. Solvency I was not consistently applied throughout EU as the directive allowed countries to implement insurance regulation in different ways. Moreover Solvency I did not consider risks fully or in detail. In life business, the major criticism was the lack of consideration of asset risks. Allowances for latest developments in risk management were also inadequate and companies could not use an internal model to calculate the solvency capital. Finally, the increasing presence of conglomerates and groups forced the insurance regulator to align some requirements with the banking regulation, Basel II/III. Due to the differences in their core business activities, banks and insurers regulators’ goal does not imply comparability of the overall capital charges. However, considering the asset side of the balance sheets, the investment portfolios of banks and insurers contain the same asset classes. In order to avoid regulatory arbitrage, the capital charges for the same amount and type of asset risk should be similar. Chapter 2 compares the main regulatory frameworks in Europe: Solvency II and the Swiss Solvency Test, SST, in Switzerland, with a focus on potential market implications. Both systems are quite advanced but some key differences need to be highlighted, including the treatment of assets, in particular sovereign bonds, the consideration of diversification or the risk measure applied. Solvency II uses a Value at Risk at 99.5% whereas the SST is based on a Tail Value at Risk at 99%. Our approach is both qualitative and quantitative. In particular, based on a numerical example, we aim at quantifying the level of regulatory capital prescribed by the standard models. The numerical analysis reveals large differences between capital charges assigned to the same asset class under Solvency II and the SST. Solvency II penalizes investment in stocks, mainly due to a lower diversification benefit under the standard formula. On the other hand the SST model requires a higher capital for bonds, primary due to a stringent risk measure and confidence level. The treatment of EU sovereign bonds under Solvency II is another area of concern as it does not require any capital for spread risk. The question arises to what extent an internal model leads to different capital requirements as compared to the SST and Solvency II models. Therefore we apply an internal approach based on Monte Carlo simulation to derive the necessary capital based on the Value at Risk at 99.5% (in line with the Solvency II standard model) and on the Tail Value at Risk at 99% (in line with the SST standard model). Internal models calculate capital requirements that more closely matches risks of insurers and promote a culture of risk management. To develop internal models, companies need incentives to properly manage their risks, i.e. decreasing capital requirements. One potential benefit of the standard model is that insurers who use it can be compared to one another, whereas internal models are by definition specific to individual insurers. One argument against the standard model is the possibility of some systemic risk. An unusual event in the capital or insurance market could encourage all insurers to take the exact same response, thereby causing a run in the market. The analysis shows that standard and internal models still display large discrepancies in their results, suggesting a long way ahead to achieve a harmonized view between the regulators and the insurance sector. The choice of a statistical model or the refinement of parameters are key concepts when setting up an internal model and appear to be critical in the Solvency Capital Requirement calculation. By calculating and comparing the market risk capital charges for a representative insurer under the Solvency II and the SST standard approach as well as an internal model, we are able to provide evidence that the regulatory framework might have an impact on asset portfolios. The main impacts would be a shift from long-term to shorter-term debt, an increase in the attractiveness of higher-rated corporate debt and government bonds, in particular EU sovereign bonds as the consequence of the special treatment under Solvency II, as well as low level of equity holdings. But it is unlikely that large-scale reallocations will happen in the short term, as transitional arrangements are likely to phase in the implementation of Solvency II over several years. The likely impact on assets portfolios could have also already been anticipating by insurers. Chapter 3 studies the effectiveness of the Solvency II reform to prevent the default probability faced by a life insurance company. The default risk leads to a consequence that policyholders might not get back their initial investment upon default of the insurance company. Therefore, policyholders are concerned with the issues like what probability the insurance company will become bankrupt and which amount they can expect to obtain after taking account of the default risk of the insurer. Starting from a theoretical life insurance company which sells a participation insurance policy containing only a savings component and a single premium inflow, we simulate a life insurance company on an eight-year time horizon. We focus only on market risks as there is no mortality risk attached to the insurance contract. Finally several policies and investment strategies will be analysed. The purpose of the chapter is to evaluate how Solvency II can prevent the company to collapse. The papers discussing Solvency II effectiveness are qualitative in nature. In particular there is little research on the accuracy of the standard formula with regard to the proclaimed ruin probability of 0.5% per year. To do so we compare the probability of default at maturity of the life insurance policy, i.e. if the company has to enough assets to pay what was promised to the policyholders, with the early probability of default forced by Solvency II based on standard and internal models. We have first to calculate the Solvency Capital Requirement as laid down in the directive. One crucial point is the evaluation of liabilities. To do so we use an approach recently applied by the insurance sector called Least-squares Monte Carlo (LSMC). The aim of Solvency II is to monitor insurers on an annual basis. The SCR level can then be interpreted as a regulatory barrier, consistent with a model developed by Grosen and Jørgensen (2002). Key drivers of the ruin probability at maturity include interest rate parameters, portfolio riskiness and investment strategies in bonds. The continuously decrease of interest rates creates a challenge for insurers, especially life insurers that suffer a double impact on their balance sheet: a valuation effect and a decreasing reinvestment returns of premiums and maturing bonds. The latter explain also the riskiness of rolling-bond strategies compared to duration matching strategies. By setting the confidence level to 99.5% per year, the regulator wants to ensure that the annual ruin probability equals to 0.5%. Since the SCR from our internal model equals the 0.5% quantile of the distribution, it exactly matches the targeted ruin probability. Our analysis reveals that the set-up and calibration of the Solvency II standard model are inadequate as the solvency capital derived by the standard formula overestimates the results of the internal model. This is mainly the consequence of an overestimated equity capital and a lower diversification benefit. The 0.5% proclaimed goal under Solvency II is not reached, being too conservative. One declared goal of the directive is to decrease the duration gap between assets and liabilities. Solvency II penalizes then rolling-bond strategies. The long-term feature of our policy should impact the level of regulatory capital. As Solvency II is based on a quantile measurement, we define the solvency capital using the default probability objective for different horizons. SCR is not systematically a decreasing function of the time horizon even if a decreasing form appears on long-term. This shows undoubtedly that a horizon effect exists in terms of measurement of solvency. As the standard model overestimated the internal model capital we expect a forced default probability higher than 0.5% under the Solvency II framework. The SCR barrier stops the company more often than it should be. This can be interpreted as one cost of regulation, i.e. closing down financially sound at maturity companies. The analysis of the evolution of default probabilities as a function of time horizon reveals that ruin probabilities at maturity lie always below the Solvency II objective. Furthermore the gap between the observed default at maturity and the Solvency II objective is increasing over time; the situation is even worse for longer-term insurance products. Finally stakeholders are more interested in their expected return than in the default probability. A cost of regulation defined as the difference between stakeholder’s returns with and without regulatory framework exists, particularly for shareholders. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

This thesis is dedicated to Solvency II, a regulatory framework for insurance and reinsurance companies effective in European Union. Firstly, it explains the notion solvency and also describes the principles of the regulation itself. Another part is focused on the calculation of solvency capital requirement and minimal capital requirement, using standard formula. The capital requirements are derived on the level of risk modules and their submodules. Furthermore, the topic of technical reserves is discussed and emphasis is placed on the derivation of mean square error of prediction. Described methods are Chain-Ladder and Bornhuetter-Ferguson. The last part of the thesis includes the calculation of capital requirements for real data. A program SolvencyII.xlsx that shows particular derivations is enclosed.