
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)


Essays on Finance and Risk
Kowalczyk, Dorota ; Zemčík, Petr (advisor) ; Poghosyan, Tigran (referee) ; Vecer, Jan (referee)
Dorota Kowalczyk: Essays on Finance and Risk Abstract This dissertation consists of three chapters that empirically investigate questions of increasing relevance in the banking risk and financial economics literature. The first chapter studies bank risk in the context of its joint determination with bank liquidity and capital in the Eurozone. The second chapter examines the banks' appetite for risk using the comprehensive credit register of the Czech National Bank. Finally, the last chapter refers to model risk and analyzes the ability of the selected term structure models to value the interest rate swaps in the Polish market. The first chapter analyzes the coordination of bank risk, liquidity and capital in the presence of securitization. Its outcome contributes to the debate on the effectiveness of the banking regulations. My findings with regard to the simultaneity of capital and risk decisions are consistent with previous empirical studies. Incorporation of bank liquidity permits me to establish the presence of the coordination of risk and liquidity decisions. At the same time, I find no evidence of the direct joint determination of capital and liquidity. Finally, the first chapter partially confirms the theoretical implications of Repullo (2005). The second chapter, coauthored with Adam Geršl, Petr...


Stochastic Models in Financial Mathematics
Waczulík, Oliver ; Hurt, Jan (advisor) ; Večeř, Jan (referee)
Title: Stochastic Models in Financial Mathematics Author: Bc. Oliver Waczulík Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathe matical Statistics Abstract: This thesis looks into the problems of ordinary stochastic models used in financial mathematics, which are often influenced by unrealistic assumptions of Brownian motion. The thesis deals with and suggests more sophisticated alternatives to Brownian motion models. By applying the fractional Brownian motion we derive a modification of the BlackScholes pricing formula for a mixed fractional Bro wnian motion. We use Lévy processes to introduce subordinated stable process of OrnsteinUhlenbeck type serving for modeling interest rates. We present the calibration procedures for these models along with a simulation study for estima tion of Hurst parameter. To illustrate the practical use of the models introduced in the paper we have used real financial data and custom procedures program med in the system Wolfram Mathematica. We have achieved almost 90% decline in the value of KolmogorovSmirnov statistics by the application of subordinated stable process of OrnsteinUhlenbeck type for the historical values of the monthly PRIBOR (Prague Interbank Offered Rate) rates in...


Analysis and prediction of league games results
Šimsa, Filip ; Hanzák, Tomáš (advisor) ; Večeř, Jan (referee)
The thesis is devoted to an analysis of ice hockey matches results in the highest Czech league competition in seasons 1999/2000 to 2014/2015 and to prediction of the following matches. We describe and apply Kalman filter theory where forms of teams represent an unobservable state vector and results of matches serve as measurements. Goal differences are identified as a suitable transformation of a match result. They are used as a dependent variable in a linear regression to find significant predictors. For a prediction of a match result we construct an ordinal model with those predictors. By using generalized Gini coefficient, we compare a diversifica tion power of this model with betting odds, which are offered by betting companies. At the end, we combine knowledge of odds before a match with other predictors to make a prediction model. This model is used to identify profitable bets. 1

 

Order book dynamics
Peržina, Vít ; Swart, Jan (advisor) ; Večeř, Jan (referee)
Main goal of this thesis is improvement of an order book model so that it behaved more realistically, based on a model developed by J. Plačková in her diploma thesis in 2011. We consider this simple model for evolution of order book in which limit orders of unit size arrive according to independent Poisson processes. Frequency of buy limit orders below resp. sell limit orders above a given price level is described by demand and supply functions. Buy (resp. sell) limit orders that arrive with price above (resp. below) the current ask (resp. bid) price are converted into market orders and cancellation of orders is not allowed. We extend this model by introducing market makers who place at the same time one buy and one sell limit order with current bid and ask prices. We show how introducing market makers reduces the spread that in the original model was unrealistically large and also show a method of calculating the precise rate of market makers needed to reduce the spread to zero. 1
