|
|
The Role of Advanced Option Pricing Techniques Empirical Tests on Neural Networks
Brejcha, Jiří ; Baruník, Jozef (advisor) ; Vošvrda, Miloslav (referee)
This thesis concerns with a comparison of two advanced option-pricing techniques applied on European-style DAX index options. Specifically, the study examines the performance of both the stochastic volatility model based on asymmetric nonlinear GARCH, which was proposed by Heston and Nandi (2000), and the artificial neural network, where the conventional Black-Scholes-Merton model serves as a benchmark. These option-pricing models are tested with the use of the dataset covering the period 3rd July 2006 - 30th October 2009 as well as of its two subsets labelled as "before crisis" and "in crisis" data where the breakthrough day is the 17th March 2008. Finding the most appropriate option-pricing method for the whole periods as well as for both the "before crisis" and the "in crisis" datasets is the main focus of this work. The first two chapters introduce core issues involved in option pricing, while the subsequent third section provides a theoretical background related to all of above-mentioned pricing methods. At the same time, the reader is provided with an overview of the theoretical frameworks of various nonlinear optimization techniques, i.e. descent gradient, quassi-Newton method, Backpropagation and Levenberg-Marquardt algorithm. The empirical part of the thesis then shows that none of the...
|
|
|
Advanced methods of interest rate models calibration
Holotňáková, Dominika ; Witzany, Jiří (advisor) ; Branda, Martin (referee)
This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1
|
|
|
Continuous market models with stochastic volatility
Petrovič, Martin ; Maslowski, Bohdan (advisor) ; Hlubinka, Daniel (referee)
Vilela Mendes et al. (2015), based on the discovery of long-range dependence in the volatility of stock returns, proposed a stochastic volatility continuous mar- ket model where the volatility is given as a transform of the fractional Brownian motion (fBm) and studied its No-Arbitrage and completeness properties under va- rious assumptions. We investigate the possibility of generalization of their results from fBm to a wider class of Hermite processes. We have reworked and completed the proofs of the propositions in the cited article. Under the assumption of indepen- dence of the stock price and volatility driving processes the model is arbitrage-free. However, apart from a case of a special relation between the drift and the volatility, the model is proved to be incomplete. Under a different assumption that there is only one source of randomness in the model and the volatility driving process is bounded, the model is arbitrage-free and complete. All the above results apply to any Hermite process driving the volatility. 1
|
|
|
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).
|
|
|
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
|
|
|
Advanced methods of interest rate models calibration
Holotňáková, Dominika ; Witzany, Jiří (advisor) ; Branda, Martin (referee)
This thesis is focused on the study of advanced methods of interest rate mo- dels calibration. The theoretical part provides introduction to basic terminology of financial mathematics, financial, concretely interest rate derivatives. It presents interest rate models, it is mainly aimed at HJM approach and describes in detail the Libor market model, then introduces the use of Bayesian principle in calcula- ting the probability of MCMC methods. At the end of this section the methods of calibration of volatility to market data are described. The last chapter consists of the practical application of different methods of calibration Libor market model and consequently pricing od interest rate swaption. The introduction describes procedure of arrangement of input data and process of pricing of interest rate derivatives. It is consequently used for the valuation of derivative contract accor- ding to mentioned methods. 1
|
|
|
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
|
|
|
The Role of Advanced Option Pricing Techniques Empirical Tests on Neural Networks
Brejcha, Jiří ; Baruník, Jozef (advisor) ; Vošvrda, Miloslav (referee)
This thesis concerns with a comparison of two advanced option-pricing techniques applied on European-style DAX index options. Specifically, the study examines the performance of both the stochastic volatility model based on asymmetric nonlinear GARCH, which was proposed by Heston and Nandi (2000), and the artificial neural network, where the conventional Black-Scholes-Merton model serves as a benchmark. These option-pricing models are tested with the use of the dataset covering the period 3rd July 2006 - 30th October 2009 as well as of its two subsets labelled as "before crisis" and "in crisis" data where the breakthrough day is the 17th March 2008. Finding the most appropriate option-pricing method for the whole periods as well as for both the "before crisis" and the "in crisis" datasets is the main focus of this work. The first two chapters introduce core issues involved in option pricing, while the subsequent third section provides a theoretical background related to all of above-mentioned pricing methods. At the same time, the reader is provided with an overview of the theoretical frameworks of various nonlinear optimization techniques, i.e. descent gradient, quassi-Newton method, Backpropagation and Levenberg-Marquardt algorithm. The empirical part of the thesis then shows that none of the...
|
|
|
Methods of volatility estimation
Hrbek, Filip ; Witzany, Jiří (advisor) ; Fičura, Milan (referee)
In this masterthesis I have rewied basic approaches to volatility estimating. These approaches are based on classical and Bayesian statistics. I have applied the volatility models for the purpose of volatility forecasting of a different foreign exchange (EURUSD, GBPUSD and CZKEUR) in the different period (from a second period to a day period). I formulate the models EWMA, GARCH, EGARCH, IGARCH, GJRGARCH, jump diffuison with constant volatility and jump diffusion model with stochastic volatility. I also proposed an MCMC algorithm in order to estimate the Bayesian models. All the models we estimated as univariate models. I compared the models according to Mincer Zarnowitz regression. The most successfull model is the jump diffusion model with a stochastic volatility. On the second place they were the GJR- GARCH model and the jump diffusion model with a constant volatility. But the jump diffusion model with a constat volatilit provided much more overvalued results.The rest of the models were even worse. From the rest the IGARCH model is the best but provided undervalued results. All these findings correspond with R squared coefficient.
|
|
|
Option pricing under stochastic volatility
Khmelevskiy, Vadim ; Fičura, Milan (advisor) ; Janda, Karel (referee)
This master's thesis focuses on the problem area of option pricing under stochastic volatility. The theoretical part includes terms that are essential for understanding the problem area of option pricing and explains particular models for both option pricing under stochastic volatility and those under constant volatility. The application of described models is performed in the practical part of the thesis. After that particular models are compared to the real data.
|
guest ::
