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Stable distribution and application to finance
Omelchenko, Vadym ; Branda, Martin (referee) ; Klebanov, Lev (advisor)
Title: Stable distributions and application to finance Author: Vadym Omelchenko Department: Department of Probability and Mathematical Statistics Supervisor: Prof. Lev Klebanov, DrSc. Supervisor's e-mail address: Lev.Klebanov@mff.cuni.cz Abstract: This work deals with the theory of the stable distributions, their parameter estimation, and their financial application. There arc given the methods of characteristic function and method of projections, which is rel- ative to ML-methodology, for estimation of the parameters of stable dis- tributions. We compare these methods with the conventional estimators. The quality of estimators is verified by the simulation of the sample having stable distribution with known parameters and comparing the estimates of these parameters with their real values. The aim of this work is estima- tion of parameters of the stable laws which iy applicable for modification of AHCH/GAHCH models with stable innovations. Keywords: stable distribution, ARGII/GARCII models, characteristic func- tion (CF) based estimators, maximum likelihood projection (MLP) estima- tors.
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Risk measures - sensitivity and dynamics
Branda, Martin ; Polívka, Jan (referee) ; Lachout, Petr (advisor)
Risk measures are subject to many scientific papers and monographs published on financial portfolio optimization problem within stochastic programming. Currently there are many functionals which measure risk of random future losses according to risk managers preferences. However, their sensitivity is studied less commonly, especially according to possible changes of input data or with respect to the portfolio allocation. This thesis deals with sensitivity of two frequently discussed measures - Value at Risk (VaR) and Conditional Value at Risk (CVaR). Explicit contamination bounds for relative VaR optimization problem are expressed using general results of parametric optimization valid for quadratic programming. A numerical study and a heuristic algorithm for correlation matrices stressing are involved. Sensitivity of VaR and CVaR is studied through their derivatives with respect to the portfolio allocation. Assumptions for the derivatives are formulated, Hessians introduced and convexity is discussed. At last, some dynamic risk measures for multi-period investory models are proposed.
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Multivariate GARCH
Maďar, Milan ; Hurt, Jan (advisor) ; Branda, Martin (referee) ; Mazurová, Lucie (referee)
4 Title: Multivariate GARCH Author: Mgr. Milan Mad'ar Department: Katedra pravděpodobnosti a matematické statistiky Abstract: This thesis will examine the regional and global linkages as evi- dence of integration of stock markets in Frankfurt, Amsterdam, Prague and the U.S. Therefore we will utilize the multivariate GARCH approach that investigates the dynamics of volatility transmission of related foreign exchange rates. Also, we will define three basic model classes. For each of the model classes a theoret- ical review, basic properties and estimation procedure with proofs are provided. We illustrate each approach by applying the models to daily market data. The two main aims of the thesis are to discuss and report the existence of regional and global stock markets linkages and provide a comparison of such multivariate GARCH models on the data sample. The main contribution of the thesis is that it treats the data in the context of real development in financial markets and takes into account the real situation during and after the financial crisis of 2008. We find out that the estimated time-varying conditional correlations indicate limited integration among the markets, which implies that investors can benefit from the risk reduction by investing in the different stock markets, especially during the crisis....
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Traditional and modern approaches to pricing in nonlife insurance
Vojtěch, Jonáš ; Branda, Martin (advisor) ; Mazurová, Lucie (referee)
Title: Traditional and modern approaches to pricing in nonlife insurance Abstract: This thesis deals with the theory and implementation of generalized linear models in the area of pricing of non-life insurance and subsequent optimalization of rates. Using the generalized linear models it is possible to estimate expected value and variance of compound distribution of total claims made according to insurance policy during definite time period. The next step is to build an optimalization model and describe several methods how to determine rates that lead to optimal distribution of safety margins within insurance policies in particular risk groups. Represented approaches how to calculate insurance premiums are numerically illustrated on simulated data in concluding parts of the thesis.
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Sparse robust portfolio optimization via NLP regularizations
Branda, Martin ; Červinka, Michal ; Schwartz, A.
We deal with investment problems where we minimize a risk measure\nunder a condition on the sparsity of the portfolio. Various risk measures\nare considered including Value-at-Risk and Conditional Value-at-Risk\nunder normal distribution of returns and their robust counterparts are\nderived under moment conditions, all leading to nonconvex objective\nfunctions. We propose four solution approaches: a mixed-integer formulation,\na relaxation of an alternative mixed-integer reformulation and\ntwo NLP regularizations. In a numerical study, we compare their computational\nperformance on a large number of simulated instances taken\nfrom the literature.
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Day-ahead bidding on energy markets - a basic model and its extension to bidding curve
Branda, Martin
Wind resources energy production is highly influenced by uncertain weather conditions. We provide several simple models for bidding on day-ahead energy markets, which take into account the uncertainty. The obtained optimal bids and bidding curve are based not only on the point prediction, but also on the forecasted distribution of generated energy. We relate the resulting problems to two-stage stochastic programs with simple recourse.
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Influence of short sales and margin requirements on portfolio efficiency - a DEA-risk approach
Branda, Martin
We focus on efficiency of assets and portfolios available to investors on financial markets. We employ diversification consistent DEA-risk models with CVaR deviations as the inputs and expected rate of return as the output. Moreover, we allow short selling and take into account margin requirements. Our model is then employed in an empirical study where selected assets from US stock market are investigated. The sample approximation technique is used to deal with the multivariate skew-normal distribution of random returns.
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Managing financial risks in an insurence company
Čech, Tomáš ; Marek, Luboš (advisor) ; Branda, Martin (referee)
The graduation thesis addresses the problems of managing and measuring of financial risks in activities of insurance companies. The first chapter handles the definitions of the financial risk and it classification. The second chapter defines a random variable returns of measure of financial assets. Sets up formulas of the return measure and also focuses on problem of time aggregation. The third chapter theoretically describes methodology of value at risk as the most widely used method for measuring and managing risk by insurance companies and regulatory authority. The fourth chapter contains an empirical study from practice which compares the two basic method of computing value at risk. The fifth chapter is the main part of the graduation thesis and focuses on verifying of the model and his imperfections. It verifies also achievements of initial assumptions. The sixth chapter targets on possibilities of extension value at risk method by liquidity risk incorporation.
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