|
|
Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
|
|
|
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
|
|
|
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.
|
|
|
Models of integer-valued time series
Houfková, Lucia
13311971730966-1666e6a7843fe8fa35041013336015b3.txt Abstract Title: Models of integer-valued time series Author: Lucia Jarešová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Supervisor's e-mail address: praskova@karlin.mff.cuni.cz Abstract: In the presented work the generalized integer valued processes GINAR founded on the Steutel and van Harn generalized operator are studied. Proper- ties of this operator, which are based on the sum of i.i.d. random variables are investigated including the determination of the domain of the operator and sug- gestion of possible construction of this operator. The attention is given on a weak stationary GINAR(p), the main properties of this process are described and it is shown that this process has an AR(p) representation, where the white noise consists of martingale differences. Further, the parameter estimators are descri- bed and consequently tested on extensive simulation with differently distributed innovations. The results are compared according to MSE. The work also contains a real data application. At the end the vector processes VGINAR are mentio- ned, that can also have a VAR representation. The functions for the program environment R are included. Keywords: GINAR, VGINAR, Steutel and van Harn...
|
|
|
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.
|
|
|
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.
|
|
|
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.
|
|
|
Interest Rate Risk Analysis by Principal Component Method
Myšičková, Ivana ; Houfková, Lucia (advisor) ; Prášková, Zuzana (referee)
Presented study analyzes interest rate risk associated with the possession of given fixed coupon bond. In the first chapter, we define some of the basic concepts and provide description of available data. These are historical data on spot interest rates of zero-coupon bonds for various times to maturity which will be used for the construction of the yield curves. Based on these bond yield curves we evaluate the bond, thus obtaining a picture of the evolution of its price. Later on, we try to estimate its price tomorrow. We present two approaches how to deal with this problem. First approach is the normal interest rate risk analysis based on duration and convexity, second approach is the method of principal components which will be applied to the historical daily changes in yield curves. The method of principal components is introduced in detail.
|
|
|
Models of integer-valued time series
Houfková, Lucia
13311971730966-1666e6a7843fe8fa35041013336015b3.txt Abstract Title: Models of integer-valued time series Author: Lucia Jarešová Department: Department of Probability and Mathematical Statistics Supervisor: Doc. RNDr. Zuzana Prášková, CSc. Supervisor's e-mail address: praskova@karlin.mff.cuni.cz Abstract: In the presented work the generalized integer valued processes GINAR founded on the Steutel and van Harn generalized operator are studied. Proper- ties of this operator, which are based on the sum of i.i.d. random variables are investigated including the determination of the domain of the operator and sug- gestion of possible construction of this operator. The attention is given on a weak stationary GINAR(p), the main properties of this process are described and it is shown that this process has an AR(p) representation, where the white noise consists of martingale differences. Further, the parameter estimators are descri- bed and consequently tested on extensive simulation with differently distributed innovations. The results are compared according to MSE. The work also contains a real data application. At the end the vector processes VGINAR are mentio- ned, that can also have a VAR representation. The functions for the program environment R are included. Keywords: GINAR, VGINAR, Steutel and van Harn...
|
|
|
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
|
guest ::
