|
|
Shadow prices and portfolio management with proportional transaction costs
Klůjová, Jana ; Dostál, Petr (advisor) ; Beneš, Viktor (referee)
The diploma thesis describes portfolio management with proportional transaction costs. The main aim is to describe using of shadow prices to find the optimal Markov policies keeping the proportion of the investor's wealth invested in the risky asset within the corresponding interval in order to maximize the long run geometric growth rate. On the real market, the investor must pay transaction costs when he buys/sells shares. In the diploma thesis we transform these prices into the shadow price; when trading in the shadow price there are no transaction costs. The solution itself is based on Itô formula and the martingal theory. The prices of shares are modeled as geometric Brownian motion. Powered by TCPDF (www.tcpdf.org)
|
|
|
Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
|
|
|
Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Pešta, Michal (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
|
|
|
Asian Perpetuities
Svoboda, Miroslav ; Večeř, Jan (advisor) ; Čoupek, Petr (referee)
This Master thesis studies Asian perpetuities, which is a term standing for European type of options with an average asset as the underlying asset and the execution time of the option in infinity. Assuming Geometric Brownian motion model of price of an asset, the goal of this thesis is to study behavior of the average of the asset price. Three different types of averaging are considered: arithmetic, geometric and harmonic average. The average values of the log-normals maintain the known distribution only for the geometric average. As it is shown in the thesis; however, when the average is examined on infinite time horizon, the arithmetic and harmonic averages maintain the inverse gamma distribution or gamma distribution, respectively. This result enables the computation of the price of Asian perpetuity which is also examined in the thesis. 1
|
|
|
Asian Perpetuities
Svoboda, Miroslav ; Večeř, Jan (advisor) ; Čoupek, Petr (referee)
This Master thesis studies the Asian perpetuity, which is the European type option with the average asset as the underlying asset and the execution time of the option in infinity. Assuming the geometric Brownian motion model of an asset, the thesis studies the behavior of the average of the asset. Three different types of averaging are considered: arithmetic, geometric and harmonic average. The average values of the log-normals maintain the known distribution only for the geometric average but, as it is shown in the thesis, when the average is examined on infinite time horizon, the arithmetic and harmonic averages maintain the inverse gamma distribution or gamma distribution, respectively. This result enables the computation of the price of Asian perpetuity which is also examined in the thesis. 1
|
|
|
Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Pešta, Michal (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
|
|
|
The fast Fourier transform and its applications to European spread option pricing
Bladyko, Daniil ; Stádník, Bohumil (advisor) ; Fleischmann, Luboš (referee)
This master thesis should provide reader with an overview of the European spread options evaluation using the fast Fourier transform numerical method. The first and second part of the thesis deal with the theoretical foundations of Fourier analysis and existing approaches of spread option valuation under two and three-factors frameworks (namely GBM - geometric Brown motion and SV - stochastic volatility). The third part describes extention of Hurd-Zhou (2010) valuation method by tool for call and put spread options pricing in case of negative or zero strikes. Extension will be compared with Monte Carlo simulation results from a variety of perspectives, including computing complexity and implementation requirements. Dempster-Hong model, Hurd-Zhou model and Monte Carlo simulation are implemented and tested in R (programming language).
|
|
|
Estimations of risk with respect to monthly horizon based on the two-year time series
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Zichová, Jitka (referee)
The thesis describes commonly used measures of risk, such as volatility, Value at Risk (VaR) and Expected Shortfall (ES), and is tasked with creating models for measuring market risk. It is concerned with the risk over daily and over monthly horizons and shows the shortcomings of a square-root-of-time approach for converting VaR and ES between horizons. Parametric models, geometric Brownian motion (GBM) and GARCH process, and non-parametric models, historical simulation (HS) and some its possible improvements, are presented. The application of these mentioned models is demonstrated using real data. The accuracy of VaR models is proved through backtesting and the results are discussed. Part of this thesis is also a simulation study, which reveals the precision of VaR and ES estimates.
|
|
|
Shadow prices and portfolio management with proportional transaction costs
Klůjová, Jana ; Dostál, Petr (advisor) ; Beneš, Viktor (referee)
The diploma thesis describes portfolio management with proportional transaction costs. The main aim is to describe using of shadow prices to find the optimal Markov policies keeping the proportion of the investor's wealth invested in the risky asset within the corresponding interval in order to maximize the long run geometric growth rate. On the real market, the investor must pay transaction costs when he buys/sells shares. In the diploma thesis we transform these prices into the shadow price; when trading in the shadow price there are no transaction costs. The solution itself is based on Itô formula and the martingal theory. The prices of shares are modeled as geometric Brownian motion. Powered by TCPDF (www.tcpdf.org)
|
guest ::
