G22 - Insurance; Insurance Companies; Actuarial StudiesNávrat zpět

Catastrophic natural events in the Czech Republic have always caused a considerable burden on public finance. However, this risk can be transferred to capital market investors through CAT bonds, which have never been used for this purpose in the Czech Republic. The paper deals with the theoretical background of CAT bonds, resulting in a back test simulation of a hypothetical CAT bond issued for the period 1999-2003. As a result, by transferring the risk to the capital market, investors could save a significant part of the Czech Republic's public funds.

This paper examines the impact of financial market development, financial crises and deposit insurance on bank risk based on macro data of 86 countries during the period 1998-2014. The results show that banking sector development and stock market development have opposing effects on bank risk measured as bank non-performing loan ratio. The introduction of an explicit deposit insurance system plays a significant role in reducing banks’ risk. However, the bank market development after the introduction of this system also increases banks’ risk. The impact of financial market development and deposit insurance system on banks’ risk was more significant before the 2008 financial crisis. It is found that there is a nonlinear relationship between financial market development, deposit insurance, financial crises and banks’ risk. The stock market development has an asymmetric effect on banks’ risk.

This analysis tries to address the problem of the insufficiency of premium rates used by export credit agencies. This paper aims to answer why and how states should run agencies that may create losses. We see that each supported exporter brings some other benefits to the public budget, and we try to propose how it could be measured. This paper therefore focuses on benefits and costs of the domestic economy. This analysis aims to develop a model that calculates the impacts of each supported export project. The results must be comparable between projects so that projects can be ranked and decisions made on which ones should receive support under current capacity restraints. The current state of knowledge has been analysed, and little attention has been paid to this microeconomic area of export support. The model structure also helps us understand why governments tend to maintain export credit agencies even though they may be temporarily loss-making.

Equity release contracts allow property owners to receive a financial benefit in exchange for surrendering their real estate to a company. The benefits depend on the life expectancy of owners, the real value of properties, and the rate of interest. These parameters are not the same throughout the years. The aim of the paper is to analyse varying payments of equity release contracts which have already been offered to customers for several years in Poland. A recalculation procedure year by year is proposed applying the actuarial and financial methods. This paper estimates the potential advantages of reverse annuity and reverse mortgage contracts in a changing economic environment. The calculations were made based on actual Polish market data, including the Svensson model of spot interest rate. It is shown that there is considerable scope for increasing retirement income; however, the exact amounts may be unknown. The advantages for customers resulting from changes in parameters and valorization are shown, as well as the risk associated with equity release.

This article aims to analyse the issue of a lack of rules on the insurance cover of interest from an OECD perspective during the period 2010-2020. Export credit agencies (ECAs) support export and apply minimum premium rates (MPRs) to the principal amount only, while the insurance agreement covers also the interest amount. This area can be described as a grey zone, because ECAs can decide themselves what cover they provide for a limited price. This paper explains which parts of a lending rate should be covered under credit insurance and provides theoretical and empirical analysis of the maximum extent of interest cover. The extent of such cover is closely related to the return on ECAs' investments. An excessive amount of interest cover creates room for market failures such as moral hazard or adverse selection, which have a negative impact on the domestic economy. The right amount of interest cover, on the other hand, guarantees long-term sustainability and a level playing field among ECAs, as the OECD requires.

This paper focuses on national support for export and examines whether, following the OECD arrangement, long-term financial sustainability is assured without sustained fiscal help. Rules on permitted state support in this area are stated by the OECD Consensus, which is meant to guarantee a level playing field for all exporters, to encourage competition among exporters based on the quality and prices of goods, and at the same time, not distort the free market. The main objective is that every export credit agency (ECA) should be self-sustainable with no need for state subsidies. However, this may not be achieved. This research proves inadequacy of minimum premium rates (MPR) due to insured interest. This issue arises mainly from the application of MPRs to the principal value of the insured loan with no correspondence to the insured interest amount. As many ECAs are publicly owned, all systematic losses must be covered by state budgets, which is against OECD agreements and is not allowed.

This paper deals with the effects of distribution stress and macroeconomic factors on the composition of life insurance investment portfolios on the Central European market. Using a wide array of variables and the VAR model as our main method, we have found that a strong majority of insurers react to external shocks, induced by high levels of contract turnover or positive changes in macro-variables such as GDP and inflation, by strengthening bond components of their portfolio. The exception is connected to interest rates (two-week repo), which presumably have a negative effect on bond investments. Other components such as shares, funds and cash positions have been affected in a diverse way, yet to a minor extent. This implies that insurers tend to react to external stressors by beefing up the conservative part of their investments, potentially leading to an underperformance of managed assets. As such, our results point to conceivable regulatory implications, which would prevent those secondary negative detriments of life distribution growth (i.e., reselling), which are to be expected on the surveyed market.

An ageing European population and, therefore, a rising dependency ratio of retirees to the working population, strongly suggests that a pension funding gap will be a key social issue in future. Yet many older people have significant real estate assets that they could access using equity release products. They could sell their assets in exchange for lifelong or temporary monthly payments. Equity release products are relatively new to Poland, but are not yet offered by commercial banks in Czechia and Slovakia. This paper estimates the potential benefits of marriage reverse annuity, and reverse mortgage contracts, using the Svensson model function, and empirical property data from selected Czech, Slovak and Polish cities. The results are also compared to the average pension of inhabitants in the selected cities. It is shown that there is substantial scope for boosting retirement income in all the cases considered, though the precise size of the increase depends on factors such as contract buyers' age and life expectancy, the value of their assets, the payment consequences of a spouse's death, and contract suppliers' pricing policies.

We model the probabilistic structure and cash flows arising from marriage reverse annuity contracts in the case of the joint-life status and the last surviving status. In contrast to the classical approach, we take into consideration that future lifetimes between spouses are dependent. The structure of dependence of the length of spouses' lives is modelled using copulas. The term structure of interest rate is modelled using a time-dependent function. The numerical results are based on actual Polish data covering both the structure of the probabilistic model and the interest rate.

The aim of this article consists in the analysis of the beta coefficient presented in different areas for three types of financial institutions: banks, investment banks and life insurance companies. In the final evaluation, we analyse whether the beta coefficient has a high tendency to reach number one and whether there is a relatively stabilized position of the beta coefficient different from one for a certain period and a certain financial institution on a certain market and whether it is possible to avoid a relatively complicated process of beta coefficient identification in income valuation. For that reason, the analysis of the five-year beta coefficient in the years 2000-2014 was performed for the USA, developed European, emerging European, developed Asian and emerging Asian regions. The analysis proved that the beta coefficient values are lower than the "magic one", meaning that using a beta coefficient equal to one is possible only in some specific cases. Also, stability of the beta coefficient with some permitted deviation was identified only for some financial institutions and for some markets, for example 0.6 for banks on the developed Asian market and 0.35 on the US market.

Exposure curves play significant role in modelling of property per risk excess of loss non-proportional reinsurance contracts, especially in the situations when not enough historical data is available for applying experience-based methods or if the underlying exposure changed significantly. The paper deals only with the first loss scale (FLS) approach which is frequently used in Europe. An alternative approach is based on ISO´s PSOLD methodology which is typical for the U.S. The first research into FLS approach was done by Ruth E. Salzmann in 1963 and some further curves have been developed since that time, however, their availability is limited. According to the authors´ knowledge only limited number of articles were published on this topic and no comprehensive publication which would describe the methodology to a larger extent exists. The paper provides a comprehensive description of the FLS exposure rating methodology, aims to summarise both historical and latest developments in this area and also includes various authors´ own practical considerations. The theory is illustrated on numerical examples.

On a comprehensive duration data set covering 189 countries from 1960 to 2015, we employ a Heckman two-step selection model to investigate determinants of deposit insurance coverage. We find that macroeconomic status, bank structure and regulatory, political institution, legal system and deposit insurance design characteristics have a significant effect on deposit insurance coverage. Moreover, empirical results show that the impact factors are different between developing and developed countries, especially the design characteristics. Specifically, for developing countries, the scheme with the Foreign currency will support a higher coverage. And for developed countries, the Interbank deposits will lead to a lower coverage, but the No coinsurance shows the opposite effect. It is noteworthy that both the Payouts and Backstop from government influence the coverage setting conversely in different samples, which implies that there may be higher banks' risk-taking incentives in developing countries after setting up explicit deposit insurance system.

The contribution deals with the risk regulation in the framework of Solvency II, which is the new regulatory system in insurance valid in majority of the EU countries since 2016. It concentrates on the underwriting risk (in particular, on the reserve risk) and on the counterparty default risk (i.e. mainly on the reinsurers' default risk), since such risks are crucial for insurance activities. Various actuarial approaches to the underwriting risk applied by subjects respected by insurance regulators and supervisors are surveyed. Moreover, one of them suggests by means of a real data example a simplified approach to the reserve risk, which may be appreciated in practice just for its simplicity. As to the counterparty default risk, the paper presents a method that can be suitable when the reinsurers form a small group of heterogeneous subjects imperilled by a common shock as a financial crisis or a natural catastrophe; this methodological approach is also demonstrated by a numerical example.

Estimation of claims reserves, which should be held by the insurer so as to be able to meet expected future claims arising from policies currently in force and policies written in the past, presents an important task for insurance companies to predict their liabilities. A common approach to the reser-ving problem is based on generalized linear models (GLM). In this article, the application of genera-lized linear mixed models (GLMM) - an extension of the GLM - for estimation of the loss reserves is shown. Since the GLMM allows incorporating a random effect instead of several fixed effects corresponding to the accident years as in case of the GLM, volatility of the prediction is reduced. This allows more flexible risk valuation, which is a crucial element of risk management and capital allocation practices of non-life insurers. A real data example together with diagnostics for the model selection are provided as an illustration of the potential benefits of the presented approach.

The paper presents various GLM models using individual rating factors to calculate the solvency capital requirements for non-life underwriting risk in insurance. First, we consider the potential heterogeneity of claim frequency and the occurrence of large claims in the models. Second, we analyse how the distribution of frequency and severity varies depending on the modelling approach and examine how they are projected into SCR estimates according to the Solvency II Directive. In addition, we show that neglecting of large claims is as consequential as neglecting the heterogeneity of claim frequency. The claim frequency and severity are managed using generalized linear models, that is, negative-binomial and gamma regression. However, the different individual probabilities of large claims are represented by the binomial model and the large claim severity is managed using generalized Pareto distribution. The results are obtained and compared using the simulation of frequency-severity of an actual insurance portfolio.

This article aims to evaluate the research of the different published opinions on the insurance company valuation, to analyse them and to judge their use in practice. The process of the va-luation of the insurance company is very complicated and there are not many theoretical studies concerning this problem. The valuation of insurance companies should take into account the specifics of insurance activities and should look for the optimal approach. There were different approaches available - the income approach, the market comparison approach, the assets-based approach and the Bond Pricing Model. They can be combined and so there can be created different types of models. The two most important models of Massari, Gianfrate and Zanetti (2014) and Hrdý, Ducháčková (2014) were analysed and compared. Both models are applicable in practice. For the final valuation standards it could be recommended to use minimum of two methods of valuation or one of the two in detailed analysed models. Keyword: valuation, insurance company, standards, models

The aim of the article is to introduce a complex econometric model of cash-lows for the Czech life insurance market. Namely, technical-actuarial links among insurance variables observed in annually published summary balance sheets of life insurers are described by means of an econometric system of linear simultaneous equations. The suggested model is statistically veri ed and thus it can provide useful economic interpretations. Further, adjusted residual bootstrapping is introduced in this context as a straightforward alternative which can solve possible problems with questionable asymptotic distribution properties of residuals. This technique can be applied e.g. for signi cance testing purposes. Finally, an important practical illustration of scenario analysis is considered. Such an analysis might be really useful, e.g. for internal calculations of the Czech life insurers, nancial planning or stress testing in the framework of Solvency II. Two general approaches are presented: deterministic and stochastic. The second one is capable of delivering various empirical probabilities concerning possible future developments.

The problem that assets of a fund are not sufficient to cover its liabilities is of extreme importance both for its members as well as for fund managers. We show that this problem can be solved via total claims distributions and give answers to the following questions: How much money will be needed in the first pillar in order to satisfy the requirements of pensioners in a time horizon and which groups of working people should join also the second pillar because their benefits from it will be greater than those from the first pillar? Though the paper concentrates primarily on the situation with Slovakian pension funds we believe that our findings are more general. We show that the alternative methods should be used for calculation of extremes. We discuss the so-called barrier strategy for treating the surplus of an insurance company and bring some new results concerning it.

The contribution analyzes some life annuity aspects of the pension system (including commercial insurance) in the Czech Republic. In particular, the problem of sustainability, the Generation Life Tables for the pension system and the gender problem for the pensions in the Czech Republic are discussed. Such topics are important for the future of the pension system in the Czech Republic and for the necessary pension reform. Some numerical results with the Czech data concerning these aspects are presented including corresponding conclusions. Economic theory of pensions (see e.g. Sheshinski, 2005 or Uebelmesser, 2004) is not considered here.

This paper analyses possible options how to improve the risk adjustment of the health insurance system in the Czech Republic. From the possible options it argues for including pharmaceutical cost groups (PCGs) as additional risk factors since it is an improvement that can be implemented almost instantaneously. On real data from an anonymous sickness fund it confirms that predictive performance of PCGs models is consistently better than the performance of the demographic model that is currently used. The study also describes and examines the Czech health insurance market and implications of proposed changes of policy makers. Based on experience from other countries we point to a problem of risk selection if the changes are not accompanied by a tighter regulation, specifically in the form of improved risk adjustment formula.