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Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis
Jánský, Ivo ; Rippel, Milan (advisor) ; Seidler, Jakub (referee)
The thesis evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the AR and MA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting ac- curacy is evaluated on the out-of-sample data, which are more volatile. The main aim of the thesis is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index sepa- rately. Unlike other works in this eld of study, the thesis does not assume the log-returns to be normally distributed and does not explicitly select a partic- ular conditional volatility process. Moreover, the thesis takes advantage of a less known conditional coverage framework for the measurement of forecasting accuracy.
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Two-stage backtesting of Value-at-Risk models
Matyáš, Jan ; Seidler, Jakub (advisor) ; Brechler, Josef (referee)
Bachelor Thesis Two-stage backtesting of Value-at-Risk models Jan Matyáš Abstract This paper deals with a comparative evaluation of various Value-at-Risk models in terms of their prediction accuracy. We use two-stage backtesting procedure to find the most robust methodology in several aspects. Backtesting framework comprises of testing properties of independence, unconditional coverage, and conditional coverage and successive stage, that uses loss function allowing us to compare the two selected models from the previous part. Four European indices are taken to represent both well developed countries (DAX, ATX) and developing countries (PX, WIG). Models are examined over the period from January 1997 to February 2014. The best performing model in our selection appears to be the historical method with a 99% confidence interval. The use of stable distribution or lower confidence interval do not produce satisfactory results. Powered by TCPDF (www.tcpdf.org)
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Value at Risk: GARCH vs. Stochatistic Volatility Models: Empirical Study
Tesárová, Viktória ; Gapko, Petr (advisor) ; Seidler, Jakub (referee)
The thesis compares GARCH volatility models and Stochastic Volatility (SV) models with Student's t distributed errors and its empirical forecasting per- formance of Value at Risk on five stock price indices: S&P, NASDAQ Com- posite, CAC, DAX and FTSE. It introduces in details the problem of SV models Maximum Likelihood examinations and suggests the newly devel- oped approach of Efficient Importance Sampling (EIS). EIS is a procedure that provides an accurate Monte Carlo evaluation of likelihood function which depends upon high-dimensional numerical integrals. Comparison analysis is divided into in-sample and out-of-sample forecast- ing performance and evaluated using standard statistical probability back- testig methods as conditional and unconditional coverage. Based on empirical analysis thesis shows that SV models can perform at least as good as GARCH models if not superior in forecasting volatility and parametric VaR. 1
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Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis
Jánský, Ivo ; Rippel, Milan (advisor) ; Seidler, Jakub (referee)
The thesis evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the AR and MA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting accuracy is evaluated on the out-of-sample data, which are more volatile. The main aim of the thesis is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index separately. Unlike other works in this field of study, the thesis does not assume the log-returns to be normally distributed and does not explicitly select a particular conditional volatility process. Moreover, the thesis takes advantage of a less known conditional coverage framework for the measurement of forecasting accuracy.
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Value at Risk: GARCH vs. Stochastic Volatility Models: Empirical Study
Tesárová, Viktória ; Gapko, Petr (advisor) ; Seidler, Jakub (referee)
The thesis compares GARCH volatility models and Stochastic Volatility (SV) models with Student's t distributed errors and its empirical forecasting per- formance of Value at Risk on five stock price indices: S&P, NASDAQ Com- posite, CAC, DAX and FTSE. It introduces in details the problem of SV models Maximum Likelihood examinations and suggests the newly devel- oped approach of Efficient Importance Sampling (EIS). EIS is a procedure that provides an accurate Monte Carlo evaluation of likelihood function which depends upon high-dimensional numerical integrals. Comparison analysis is divided into in-sample and out-of-sample forecast- ing performance and evaluated using standard statistical probability back- testig methods as conditional and unconditional coverage. Based on empirical analysis thesis shows that SV models can perform at least as good as GARCH models if not superior in forecasting volatility and parametric VaR. 1
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Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis
Jánský, Ivo ; Rippel, Milan (advisor) ; Seidler, Jakub (referee)
The thesis evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the AR and MA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting ac- curacy is evaluated on the out-of-sample data, which are more volatile. The main aim of the thesis is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index sepa- rately. Unlike other works in this eld of study, the thesis does not assume the log-returns to be normally distributed and does not explicitly select a partic- ular conditional volatility process. Moreover, the thesis takes advantage of a less known conditional coverage framework for the measurement of forecasting accuracy.
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