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Valuation of financial derivatives
Matušková, Radka ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In the present thesis we deal with several possible approaches to financial de- rivatives pricing. In the first part, we introduce the basic types of derivatives and the methods of trading. Furthermore, we present several models for the valuati- on of specific financial derivative, i.e. options. Firstly we describe Black-Scholes model in detail, which considers that the development of the underlying asset price is governed by Wiener process. Following are the jumps diffusion models that are extension of the Black-Scholes model with jumps. Then we get to jump models, which are based on Lévy processes. Finally, we will deal with the model, which considers that the development of the underlying asset price is governed by fractional Brownian motion with Hurst's coefficient greater than 1/2. All models are suplemented with sample examples. 1
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Time series and stochastic volatility in finance
Kováčová, Iveta ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
Title: Time series and stochastic volatility in finance Author: Iveta Kováčová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Jan Hurt, CSc. Supervisor's e-mail address: hurt@karlin.mff.cuni.cz Abstract: Following thesis introduces the basic characteristics of autoregressive models ARCH and GARCH. Afterwards, it describes numerical calculation of estimation of their parameters. Finally, it applies the abovementioned models on concrete financial data (exchange rate EUR/CZK) by means of the Mathematica 8.0 program.
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Backtesting of Time Series Models
Stroukalová, Marika ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
Title: Backtesting of Time Series Models Author: Marika Stroukalová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Lucia Jarešová Supervisor's e-mail address: lucia.jaresova@centrum.cz Abstract: In the present work we study the basic models of financial time series (ARMA, GARCH), we focus on parameter estimation and forecasting in estimated models. We describe the means of estimating parametres and future values in the program R. In the theoretical section we also discuss the features of financial time series, define simple returns and log returns and we introduce the benefits of the log returns. We also apply the white noise model, ARMA(1,1) and GARCH(1,1) on historic time series of logarithmic returns of chosen stock exchange indices, we also backtest 1-step ahead fore- cats and 5-step ahead forecasts and we compare the results of these models. By empirical comparison of real data we also analyze how the models reac- ted on the present financial crisis and evaluate how the normal distribution assumption for the data held up. Keywords: time series, ARMA, GARCH, backtesting. 1
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Investment strategies
Kučera, Libor ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
In this thesis we study interest rates and we introduce short rates models. Then we study interest rate dependent financial assets. Next we introduce duration and duration of portfolio of bonds. In the next part we focus on fundamental analysis. We mention its basic parts and we introduce tools used in fundamental analysis. In the last part we focus on technical analysis. We start with chart formations and then we describe indicators. We show application of indicators on data from real market.
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