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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
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Interest Rates
Holotňáková, Dominika ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
This thesis is focused on the study of interest rates, It consists of four chapters. The first chapter provides introduction to this issue, presents basic terminology and different method of interest rate process. The second chapter re- presents theoretical one-factor and two-factor models of interest rates, it is mainly aimed at Vasicek, Dothan and Cox-Ingersoll-Ross model, which are used in the practical part. The third chapter is devoted to internal bank policy, describing the most important factors influencing amount of interest rate and credit limit. The last part of the paper is the practical application of one-factor models on real data. At the beginning of the chapter, we describe methods of parameters esti- mation, which are used for individual models. Numerically estimated parameters are inputs for simulations of yield curves by these models. 1
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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
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Interest Rates
Holotňáková, Dominika ; Hurt, Jan (advisor) ; Zichová, Jitka (referee)
This thesis is focused on the study of interest rates, It consists of four chapters. The first chapter provides introduction to this issue, presents basic terminology and different method of interest rate process. The second chapter re- presents theoretical one-factor and two-factor models of interest rates, it is mainly aimed at Vasicek, Dothan and Cox-Ingersoll-Ross model, which are used in the practical part. The third chapter is devoted to internal bank policy, describing the most important factors influencing amount of interest rate and credit limit. The last part of the paper is the practical application of one-factor models on real data. At the beginning of the chapter, we describe methods of parameters esti- mation, which are used for individual models. Numerically estimated parameters are inputs for simulations of yield curves by these models. 1
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