
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


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.


Fixedodds betting and real odds
Vojtík, Jakub ; Lachout, Petr (advisor) ; Večeř, Jan (referee)
The fixedodds 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


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


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


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 fixedfor 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 singlecurve model. After the financial crisis some of the singlecurve's model assumptions were impaired and the model had to be reviewed. We call the reviewed model a multicurve 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 fixedforfloating swaps. 1


Martingale Approach to Roulette
Fornůsková, Monika ; Večeř, Jan (advisor) ; Hlubinka, Daniel (referee)
This main aim of this thesis is to compare two different strategies in Roulette  betting on a color and betting on a single number. Betting on a color represents a conservative strategy with diversified asset and betting on a number represents a more risky strategy without diversification. Distribution of the Maximum, the Last Exit Time and the Number of Visits of zero will be given for each strategy using Martingales or Markov Chains. The theoretical results will be supported by Monte Carlo simulations. Powered by TCPDF (www.tcpdf.org)


Robust methods in portfolio theory
Petrušová, Lucia ; Branda, Martin (advisor) ; Večeř, Jan (referee)
01 Abstract: This thesis is concerned with the robust methods in portfolio theory. Different risk measures used in portfolio management are introduced and the corresponding robust portfolio optimization problems are formulated. The analytical solutions of the robust portfolio optimization problem with the lower partial moments (LPM), valueatrisk (VaR) or conditional valueatrisk (CVaR), as a risk measure, are presented. The application of the worstcase conditional valueatrisk (WCVaR) to robust portfolio management is proposed. This thesis considers WCVaR in the situation where only partial information on the underlying probability distribution is available. The minimization of WCVaR under mixture distribution uncertainty, box uncertainty, and ellipsoidal uncertainty are investigated. Several numerical examples based on real market data are presented to illustrate the proposed approaches and advantage of the robust formulation over the corresponding nominal approach.


Statistical tests for VaR and CVaR
Mirtes, Lukáš ; Pešta, Michal (advisor) ; Večeř, Jan (referee)
The thesis presents test statistics of ValueatRisk and Conditional ValueatRisk. The reader is familiar with basic nonparametric estimators and their asymptotic distributions. Tests of accuracy of Valueat Risk are explained and asymptotic test of Conditional ValueatRisk is derived. The thesis is concluded by process of backtesting of ValueatRisk model using real data and computing statistical power and probability of Type I error for selected tests. Powered by TCPDF (www.tcpdf.org)


Calculation of capital requirements of market risk for options on stock's basket
Lendacký, Peter ; Myška, Petr (advisor) ; Večeř, Jan (referee)
The goal of the paper is to compare different approach in calculation of capital requirement of market risk for options on stock's basket and describe their impact on selected instrument. The first part of the paper describes possible approaches for the capital requirement calculation, namely Standardized approach and Internal model approach, and the theoretical base for option pricing. An instrument with the embedded option on equities was chosen to show the impact. Although the instrument is valued using Monte Carlo simulation, one chapter is devoted to BlackScholes model as the base model for option pricing. Powered by TCPDF (www.tcpdf.org)
