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Use of Interest Rate Models for Interest Rate Risk Management in the Czech Financial Market Environment
Cíchová Králová, Dana ; Arlt, Josef (advisor) ; Cipra, Tomáš (referee) ; Witzany, Jiří (referee)
The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.
Oceňování zajištění škodního nadměrku v neživotním pojištění
Hrevuš, Jan ; Marek, Luboš (advisor) ; Cipra, Tomáš (referee) ; Zimmermann, Pavel (referee)
Probably the most frequently used definition of reinsurance is insurance for insurance companies, by reinsurance the cedant (insurance company) cedes part of the risk to the reinsurer. Reinsurance plays nowadays a crucial role in insurance industry as it does not only reduce the reinsured's exposure, but it can also significantly reduce the required solvency capital. In past few decades various approaches to reinsurance actuarial modelling were published and many actuaries are nowadays just reinsurance specialized. The thesis provides an overview of the actuarial aspects of modelling a non-life per risk and for motor third party liability per event excess of loss reinsurance structure, according to the author's knowledge no study of such wide scope exists and various aspects have to be found in various fragmented articles published worldwide. The thesis is based on recent industry literature describing latest trends and methodologies used, the theory is compared with the praxis as the author has working experience from underwriting at CEE reinsurer and actuarial reinsurance modelling at global reinsurance broker. The sequence of topics which are dealt corresponds to sequence of the steps taken by actuary modelling reinsurance and each step is discussed in detail. Starting with data preparation and besides loss inflation, more individual claims development methods are introduced and own probabilistic model is constructed. Further, burning cost analysis and probabilistic rating focused on heavy tailed distributions are discussed. A special attention is given to exposure rating which is not commonly known discipline among actuaries outside of reinsurance industry and different methodologies for property and casualty exposure modelling are introduced including many best practice suggestions. All main approaches to the reinsurance modelling are also illustrated on either real or realistically looking data, similar to those provided by European insurance companies to their reinsurers during renewal periods.
The Issues of Employing Disadvantaged Groups on the Labour Market
Strnadová, Magdalena ; Stříteský, Marek (advisor) ; Cipra, Tomáš (referee)
The subject of the bachelor's thesis is the issue of the employment of disadvantaged groups on the labour market, primarily focusing on the employment of former prisoners on the Czech labour market. The first part of this paper discusses the importance of work in people's lives and the contribution work makes to a functional society, and defines the issues confronting that specific disadvantaged group. The second part is divided into two partial and one main objective. The two partial objectives are firstly to examine, based on analyses, the key aspects of the main problems facing former prisoners in the Czech Republic, and secondly to provide an overview of the support that such people can use to gain a foothold in the labour market. These are then followed by the main objective, which is to explore the main benefits and drawbacks of employing such people, perceived from their respective employer's point of view, and the standpoint of employers with regard to this disadvantaged group.
Modely finančních časových řad a jejich aplikace
Kladívko, Kamil ; Arlt, Josef (advisor) ; Witzany, Jiří (referee) ; Cipra, Tomáš (referee)
I study, develop and implement selected interest rate models. I begin with a simple categorization of interest rate models and with an explanation why interest rate models are useful. I explain and discuss the notion of arbitrage. I use Oldrich Vasicek's seminal model (Vasicek; 1977) to develop the idea of no-arbitrage term structure modeling. I introduce both the partial di erential equation and the risk-neutral approach to zero-coupon bond pricing. I briefly comment on affine term structure models, a general equilibrium term structure model, and HJM framework. I present the Czech Treasury yield curve estimates at a daily frequency from 1999 to the present. I use the parsimonious Nelson-Siegel model (Nelson and Siegel; 1987), for which I suggest a parameter restriction that avoids abrupt changes in parameter estimates and thus allows for the economic interpretation of the model to hold. The Nelson-Siegel model is shown to fit the Czech bond price data well without being over-parameterized. Thus, the model provides an accurate and consistent picture of the Czech Treasury yield curve evolution. The estimated parameters can be used to calculate spot rates and hence par rates, forward rates or discount function for practically any maturity. To my knowledge, consistent time series of spot rates are not available for the Czech economy. I introduce two estimation techniques of the short-rate process. I begin with the maximum likelihood estimator of a square root diff usion. A square root di usion serves as the short rate process in the famous CIR model (Cox, Ingersoll and Ross; 1985b). I develop and analyze two Matlab implementations of the estimation routine and test them on a three-month PRIBOR time series. A square root diff usion is a restricted version of, so called, CKLS di ffusion (Chan, Karolyi, Longsta and Sanders; 1992). I use the CKLS short-rate process to introduce the General Method of Moments as the second estimation technique. I discuss the numerical implementation of this method. I show the importance of the estimator of the GMM weighting matrix and question the famous empirical result about the volatility speci cation of the short-rate process. Finally, I develop a novel yield curve model, which is based on principal component analysis and nonlinear stochastic di erential equations. The model, which is not a no-arbitrage model, can be used in areas, where quantification of interest rate dynamics is needed. Examples, of such areas, are interest rate risk management, or the pro tability and risk evaluation of interest rate contingent claims, or di erent investment strategies. The model is validated by Monte Carlo simulations.
Information Extraction of Probability and Risk of Returns using Options Prices
Cícha, Martin ; Trešl, Jiří (advisor) ; Cipra, Tomáš (referee) ; Málek, Jiří (referee)
The issue of forecasting the future price of risky financial assets has attracted academia and business practice since the inception of the stock exchange. Also due to the just finished financial crisis, which was the worst crisis since the Great Depression, it is clear that research in this area has not been finished yet. On the contrary, new challenges have been raised. The main goal of the thesis is the demonstration of the significant information potential which is hidden in option market prices. These prices contain informations on probability distribution of the underlying asset returns and the risk connected with these returns. Other objectives of the thesis are the forecast of the underlying asset price distribution using parametric and nonparametric estimates, the improvement of this forecast using the utility function of the representative investor, the description of the current market sentiment and the determination of the risk premium, especially the risk premium on Czech market. The thesis deals with the forecast of the underlying asset price probability distribution implied by the current option market prices using parametric and nonparametric estimates. The resulting distribution is described by the moment characteristics which represent a valuable tool for analyzing the current market sentiment. According to the theory, the probability distribution of the underlying asset price implied by option prices is risk neutral, i.e. it applies only to risk neutral investors. The theory further implies that the distribution of real world can be derived from the risk neutral distribution using utility function of the representative investor. The inclusion of a utility function of representative investor improves the forecast of the underlying asset price distribution. Three different utility functions of traditional risk theory are used in the thesis. These functions range from the simple power function to the general function of hyperbolic absolute risk aversion (HARA). Further, Friedman-Savage utility function is used. This function allows both a risk averse investor and a risk loving investor. The thesis also answers the question: Are the current asset prices at so high level that the purchase of the asset means a gamble? The risk premium associated with investing in the risky asset is derived in the thesis. The risk premium can be understood as the premium demanded by investors for investment in a risky asset against the investment in a riskless asset. All the theoretical methods introduced in the thesis are demonstrated on real data coming from two different markets. Developing market is represented by shares of CEZ and developed market is represented by S&P 500 futures. The thesis deals with demonstrations in single point in time as well as in available history of the data. The forecasts of the underlying asset price distribution and the relating risk premium are constructed in the available data history. The goals and the objectives of the thesis have been achieved. The contribution of the thesis is the development of parametric and nonparametric methodology for estimating the underlying asset price probability distribution implied by the option market prices so that the nature of the particular market and instrument is captured. The further contribution of the thesis is the construction of the forecasts of the underlying asset price distribution and the construction of the market sentiment in the available history of data. The contribution of the thesis is also the construction of the market risk premium in the available history and the establishment of the hypothesis that the markets gamble before the crisis.
Modelování rizika rezerv v neživotním pojištění založené na neagregovaných datech
Zimmermann, Pavel ; Kahounová, Jana (advisor) ; Cipra, Tomáš (referee) ; Jedlička, Petr (referee)
Recently the eld of actuarial mathematics has experienced a large development due to a signi cant increase of demands for insurance and nancial risk quanti cation due to the fact that the implementation of a complex of rules of international reporting standards (IFRS) and solvency reporting (Solvency II) has started. It appears that the key question for solvency measuring is determination of probability distribution of future cash ows of an insurance company. Solvency is then reported through an appropriate risk measure based e.g. on a percentile of this distribution. While as present popular models are based solely on aggregated data (such as total loss development from a certain time period), the main objective of this work is to scrutinize possibilities of modelling of the reserve risk (i.e. roughly said, the distribution of the ultimate incurred value of claims that have already happened in the past) based directly on individual claims. These models have not yet become popular and to the author's knowledge an overview of such models has not been published previously. The assumptions and speci cation of the already published models were compared to the practical experience and some inadequacies were pointed out. Further more a new reserve risk model was constructed which is believed to have practically more suitable assumptions and properties than the existing models. Theoretical aspects of the new model were studied and distribution of the ultimate incurred value (the modelled variable) was derived. An emphasis was put also on practical aspects of the developed model and its applicability in the case of industrial use. Therefore some restrictive assumptions which might be considered realistic in variety of practical cases and which lead to a signi cant simpli cation of the model were identi ed throughout the work. Furthermore, algorithms to reduce the number of the necessary calculations were developed. In the last chapters of the work, an e ort was devoted to the methods of the estimation of the considered parameters respecting practical limitations (such as missing observations at the time of modelling). For this purpose, survival analysis was (amongst other methods) applied.
LIFE INSURANCE OPTIONS
Černý, Zdeněk ; Cipra, Tomáš (advisor) ; Málek, Jiří (referee)
The goal of the thesis is to present and apply mathematical tools that are necessary for proper understanding of valuation of options in life insurance. This includes basic principles of actuarial calculations based on first order assumptions and the basics of stochastic calculus used for derivatives pricing. Afterthat we discuss the difference between first and second order assumptions and apply the mathematical tools to valuation of life insurance options. Finally the appearance of life insurance options within the liability adequacy test and european law is mentioned.
Analýza nelineárních časových řad
Ditrich, Josef ; Trešl, Jiří (advisor) ; Cipra, Tomáš (referee)
Cílem této diplomové práce je analýza chování finančních časových řad vybraných z různých ekonomických oblastí. Konkrétně se jedná o dvě řady hodnot akcií a dvě řady hodnot měnových kurzů. V praktické části jde nejen o jejich analýzu a hledaní nejvhodnějšího modelu každé řady, ale také o popsání společných i rozdílných vlastností zkoumaných řad. Pozornost je soustředěna zejména na modelování podmíněného rozptylu pomocí modelů GARCH a hledání asymetrie pomocí nelineárních modelů volatility typu EGARCH a GJR-GARCH. Tyto modely jsou součástí většiny dostupných statistických softwarů. Ve druhé kapitole jsou uvedeny některé základní pojmy a definice, se kterými se lze při analýze časových řad setkat. Třetí kapitola popisuje základní stacionární a nestacionární lineární modely a aplikaci Kalmanových filtrů. Rozsáhlá čtvrtá část má za úkol přiblížit vlastnosti pěti nelineárních modelů, které jsou v literatuře často zmiňovány a které se vyskytují v mnoha modifikacích. Za ty nejdůležitější autor považuje bilineární modely, modely autoregresních náhodných koeficientů (RCA), dvojitě stochastické modely, prahové autoregresní modely (TAR) a autoregresní modely s podmíněným rozptylem (ARCH, GARCH). V páté části jsou již zmíněné aplikace modelů skupiny GARCH.
Modelování časových řad měnových kurzů
Žižka, David ; Trešl, Jiří (advisor) ; Cipra, Tomáš (referee)
Práce je zaměřena na modelování časových řad směnných kurzů pomocí modelů podmíněného rozptylu. V první části je vysvětlena teorie lineárních i nelineárních modelů volatility včetně popsání všech konkrétních modelů, které jsou v práci použity. Dále jsou zde podrobně popsány všechny testy, které jsou v práci použity. V druhé části jsou modelovány reálné časové řady směnných kurzů české koruny k amerického dolaru a k euru. Třetí část je zaměřena na ověření úrokové parity mezi Českou republikou a eurozónou. Tento vztah je ověřován pomocí Grangerovy kauzality a kointegrace časových řad.
Audit of Life Insurance Companies
Maršálek, Tomáš ; Cipra, Tomáš (advisor) ; Sosík, Petr (referee)
Cílem této práce je poskytnout ucelený přehled o auditu životní pojišťovny, včetně náznaku praktických aspektů této činnosti. Smyslem je také zdůraznit význam a nezastupitelnou funkci externího auditu jako zákonné ?pojistky? důvěryhodnosti nejen pro vlastníky pojišťovny, ale zejména pro klienty, kteří se na pojišťovnu spoléhají v nejtěžších chvílích života a nemají znalosti ani možnosti sami si ověřit, zda-li je hospodaření pojišťovny v pořádku a jejich peněžní prostředky v bezpečí

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