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Reverse mortgage
Korotkov, Daniil ; Mazurová, Lucie (advisor) ; Večeř, Jan (referee)
ČSOB Pojišťovna, a. s., člen holdingu ČSOB Veřejné 1 / 1 20.7.2018 Abstract: At this moment, reverse mortgages are relatively new products on the Czech market and this thesis deals with their problematics. In this thesis, we describe the main risks related to reverse mortgages, namely, longevity risk and adverse evolution of property prices. Analyzing these risks we are modelling the underlying property prices, their future behavior, discount factors along with studying the risk models such as vector autoregression, hedonic model, repeat-sales and Wills-Sherris model. In practical part, we focus on estimating the parameters of Lee-Carter model and autoregression model of zero-coupon government bond as well as applying the results of the estimation to calculate various characteristics of reverse mortgages.
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Market model with random inputs
Krch, Ivan ; Lachout, Petr (advisor) ; Večeř, Jan (referee)
The thesis deals with market models with random inputs represented by the newsvendor problem for which the randomness is given through a random number of customers. Presented work is divided into three chapters. In the first chapter we present the elementar newsvendor problem as stochastic programming problem with a fixed recourse. In the second chapter we present the multiplayer game theory adapted to the newsvendors problem. Moreover, in the second chapter we extend the problem by the second newsvendor on the market and in the third chapter we generalize the problem for n newsvendors on the market. We deal with the situations that arise in the chapters two and three from the game theory point of view and we study characteristics of a Nash equilibrium. Presented theory is demonstrated on illustrative examples in the ends of the two last chapters. 1
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Optimal portfolios
Vacek, Lukáš ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
In this diploma thesis, selected techniques for construction of optimal portfo- lios are presented. Risk measures and other criteria (Markowitz approach, Value at risk, Conditional value at risk, Mean absolute deviation, Spectral risk measure and Kelly criterion) are defined in the first part. We derived analytical solution for some cases of optimization problems, in some other cases there exists numeri- cal solution only however. Advantages and disadvantages, theoretical properties and practical aspects of software implementation in Wolfram Mathematica are also mentioned. Simulation methods suitable for portfolio optimization are brie- fly presented with their motivation in the second part. Multivariate distributions: normal, t-distribution and skewed t-distribution are presented in the third part with connection to optimization of portfolio with assumption of multivariate dis- tribution of financial losses. Optimization methods are illustrated on real data in the fourth part of this thesis. Analytical methods are compared with numerical ones. 1
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Machine learning with applications to finance
Mešša, Samuel ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
The impact of data driven, machine learning technologies across a wide variety of fields is undeniable. The financial industry, which relies heavily on predictive modeling being no exception. In this work we summarize two widely used machine learning models: support vector machines and neural networks, discuss their limitations and compare their performance to a more traditionally used method, namely logistic regression. Evaluation was done on two real world datasets, which were used to predict default of loan applicants and credit card holders formulated as a binary classification task. Neural networks and support vector machines either outperformed or showed comparable results to logistic regression with performance measured in receiver operator characteristic area under curve. In the second task neural networks outperformed both other models by a significant margin.
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Alternative risk measures and their applications
Drobuliak, Matúš ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
Title: Alternative risk measures and their applications Author: Matúš Drobuliak Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathe- matical Statistics Abstract: The objective of this thesis is to discuss alternative measures of risk. We focused on the expectile value at risk, which we compared with conventional risk measures - namely value at risk and conditional value at risk. We also discussed its properties from the financial point of view. A numerical illustration is included in the thesis. Keywords: Value at risk, Conditional value at risk, Quantile, Expectile, Expectile value at risk iii
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Favoritism Under Social Pressure: Evidence From English Premier League
Herrmann, Vojtěch ; Večeř, Jan (advisor) ; Hlávka, Zdeněk (referee)
The aim of this thesis is to study the extent to which the English Premier League referees are influenced by social pressure, especially by the home support and by the general popularity of the teams. Using regression analysis, we compare the actual length of the overtime, which is fully in the competence of the referee, with the predicted one from the usual game stoppages. Then we try to identify factors that contribute to any possible discrepancy. Our results suggest that the games tend to be extended beyond the expectations when the outcome of the game still can change, i.e., when the score differential at the time 90:00 is either zero or one. However, this extra extension happens almost regardless of the playing teams and thus we find no evidence for referee bias towards any specific team. However, a small bias towards the group of "Big" teams has been found, but only in the games in which the score differential was different from one.
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Fixed-odds betting and real odds
Vojtík, Jakub ; Lachout, Petr (advisor) ; Večeř, Jan (referee)
The fixed-odds betting is currently very popular. Bookmakers set the odds on sport events, which represent an amount possible to win per each unit bet. The aim of this thesis is to study whether the odds can reflect the probabilities of the outcomes of sport matches, based on which then try to tell if the same can go for the bettors and their bets. First, there are derived several models for setting the odds. Then there is constructed a hypothesis test to test a validity of one of these models. This cannot be rejected, thanks to which there is estimated the dependence of the real probabilities on the odds. It turns out that with the exception of probabilities close to 0 and 1 the estimation might work. The conclusion of the thesis is the statement that odds could a be a good indicator of the probabilities and in such case also the bets of the bettors would correspond to them. 1
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Analysis of Profitability of Major World Lotteries
Kozmík, Karel ; Večeř, Jan (advisor) ; Lachout, Petr (referee)
Lottery tickets cost the same for every given jackpot, which might present an opportunity to make a profitable bet for very high jackpots. This work analyses whether buying a lottery ticket might be profitable in the mean value, for a given number of tickets sold, for four major American and European lotteries: Mega Millions, Powerball, EuroJackpot, Euro Millions. A regression of the sales on the jackpot is carried out for the American lotteries to find out whether some combination of the jackpot and the tickets sold, which was determined to be profitable, can be expected to happen. 1
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Portfolio Management with Multiple Benchmarks
Navrátil, Robert ; Večeř, Jan (advisor) ; Pešta, Michal (referee)
Portfolio Management with Multiple Benchmarks Bc. Robert Navrátil Abstract: In this thesis, we study a maximal volatility portfolio that treats all assets in a symmetric way and related option contract. To preserve symmetry we need numeraire that treats all assets symmetrically. We choose market index with equal weights. In case of two assets we focus on a variation of a passport option on the portfolio. The optimal strategy for the investor is the mentioned maximal volatility portfolio. We extend the known optimal strategy for the option to a richer class of convex payoff functions. We also show a modification of the optimal strategy for maximizing the probability of ending above or at a desired level. We later extend the symmetric market model to case of three assets, which can be even further extended to an arbitrary number of assets. The three asset model requires more parameters than are observable from the data, however we show indistinguishably of the model on the choice of parameters under very natural conditions. Both numerical simulations and an application on real data is provided. 1
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Pricing of FRA and IRS under OIS discounting
Rolák, Martin ; Černý, Jakub (advisor) ; Večeř, Jan (referee)
The subject of this thesis is to review the pricing and valuation of forward rate agreements and fixed-for floating interest rate swaps. Firstly, we describe a pricing and valuation model that was used before the financial crisis of 2007/2008. The model is based on one curve which is used for both estimating the derivative's payoff and discounting, thus we call the model a single-curve model. After the financial crisis some of the single-curve's model assumptions were impaired and the model had to be reviewed. We call the reviewed model a multi-curve model as we nowadays need a different curve for discounting and estimating the payoffs. Both models are compared on a numerical example where we value fixed-for-floating swaps. 1
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