
Option Pricing
Moravec, Radek ; Hurt, Jan (advisor)
Title: Option Pricing Author: Radek Moravec Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Jan Hurt, CSc., Department of Probability and Mathematical Statistics In the present thesis we deal with European call option pricing using lattice approaches. We introduce a discrete market model and show a way how to find an arbitrage price of financial instruments on complete markets. It's equal to the discounted value of future expected cash flow. We present the binomial option pricing model and generalize it into multinomial model. We test the resulting formula on real market data obtained from NYSE and NASDAQ. We suggest a parameter estimate method which is based on time series of historical observations of daily close price. We compare calculated option prices with their real market value and try to explain the reasons of the differences. 1


Term structure of interest rates
Boháčková, Jana ; Hurt, Jan (advisor) ; Rusý, Tomáš (referee)
Bachelor thesis deals with interest rates and yield curves. Terms spot interest rate, forward interest rate and discount factor are established. Three models for describing yield curves are used, two parametric models: NelsonSiegel model and Svensson model and one nonparametric model: kernel estimator. Function of a yield curve is decribed for all models and for parametric models and the parameters in parametric models are also described. Eventually, all models are used on real data. 1


Modelling mortality by causes of death
Valter, Boris ; Mazurová, Lucie (advisor) ; Hurt, Jan (referee)
The aim of this thesis is to provide an overview of methods used in causeofdeath mortality analysis and to demonstrate the application on real data. In Chapter 1 we present the continuous model based on the force of mortality and review the approach using copula functions. In Chapter 2 we focus on the multinomial logit model formulated for causespecific mortality data, discuss life tables construction and derive life expectancy. In Chapter 3 we apply the multinomial logit model on the data from Czech Statistical Office. We identify the regression model, check its assumptions, present the outputs including the fitted life expectancy, and predicted mortality rates. Later in Chapter 3 we consider several stress scenarios in order to demonstrate the impact of shocked mortality rates on the life expectancy. In Chapter 4 we apply copula functions according to the methodology covered in Chapter 1 and consider causeelimination stress scenario.


Yield Curves
Korbel, Michal ; Hurt, Jan (advisor) ; Hlávka, Zdeněk (referee)
The master thesis is looking into the estimation of yield curve using two ap proaches. The first one is searching for parametric model which is able to describe the behavior of yield curve well and estimate its parameters. The parametric mo dels used in the thesis are derived from the class of models introduced by Nelson and Siegel. The second approach is nonparametric estimation of yield curves using spline smoothing and kernel smoothing. All used methods are then compared on real observed data and their suitability for various tasks and concrete available observations is considered. 1


Modelling mortality by causes of death
Valter, Boris ; Mazurová, Lucie (advisor) ; Hurt, Jan (referee)
The aim of this thesis is to provide an overview of methods used in causeofdeath mortality analysis and to demonstrate the application on real data. In Chapter 1 we present the continuous model based on the force of mortality and review the approach using copula functions. In Chapter 2 we focus on the multinomial logit model formulated for causespecific mortality data, discuss life tables construction and derive life expectancy. In Chapter 3 we apply the multinomial logit model on the data from Czech Statistical Office. We identify the regression model, check its assumptions, present the outputs including the fitted life expectancy, and predicted mortality rates. Later in Chapter 3 we consider several stress scenarios in order to demonstrate the impact of shocked mortality rates on the life expectancy.


Backtesting ValueatRisk: Comparison of selected approaches
Šedivý, Milan ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
This thesis focuses on the evaluation of different backtesting methods that are routinely applied to one of the most commonly used risk measure Value atRisk. The main goal of this thesis is to present approaches used to backtest ValueatRisk (including an introduction to common methods associated with ValueatRisk forecasting). These statistical evaluation methods are then applied to historical data from the years 2005 to 2010, during which we experienced two major financial crises. Afterwards, the output of our analysis is thoroughly discussed. 1


Backtesting ValueatRisk: Comparison of selected approaches
Šedivý, Milan ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
This thesis focuses on the evaluation of different backtesting methods that are routinely applied to one of the most commonly used risk measure Value atRisk. The main goal of this thesis is to present approaches used to backtest ValueatRisk (including an introduction to common methods associated with ValueatRisk forecasting). These statistical evaluation methods are then applied to historical data from the years 2005 to 2010, during which we experienced two major financial crises. Afterwards, the output of our analysis is thoroughly discussed. 1

 

Econometric models of national economies
Hála, Petr ; Hendrych, Radek (advisor) ; Hurt, Jan (referee)
The present thesis deals with multiple econometric equations systems which might provide a useful insight into the national economy modelling. It takes into account possible pitfalls of common practices. It introduces the theory and estimation methods of multiple econometric equations systems. It also discusses the equality of savings and investment and the theory of money. Furthermore, it briefly analyses Klein's model I from a theoretical point of view and uses the threestep least squares method in order to estimate it. Partial modifications of this model are suggested and implemented. The quality of the competitive models is evaluated employing the predictive criterion. Consequently, the canonical NK DSGE model is derived and subjected to theoretical criticism. The thesis debates doubts on the relevance of the NK IS curve and argues that Lucas's critique is still valid. A generalized method of moments is used to implement the NK DSGE model. Finally, this model is briefly compared with Klein's model I.


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, tdistribution and skewed tdistribution 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
