
Moddeling of interest rates at the financial markets
Myška, Petr ; Hurt, Jan (advisor) ; Vejmělek, Jan (referee) ; Keprta, Stanislav (referee)
Traditional Monte Carlo methods for a calculation of risk quantities (mainly VaR and TVaR) use for modeling of individual risk factors very simplified models of stochastic differential equations, where the drift and diffusion functions contain usually only one or two parameters. Such approach naturally reduces the accuracy of the final result and may significantly underestimate the risk of the portfolio. In this paper we focus on the construction of a portfolio risk model that uses nonparametric statistics theory. We shall assume the development of risk factors (specifically interest rate curve) is described by stochastic differential equation, but set minimum requirements for the drift and diffusion functions and thus better reflect the information contained in historical observations. Keywords: stochastic process, nonparametric estimation, diffusion, drift, local time, VaR, TVaR


Semimarkov model for credit risk management
Benková, Markéta ; Mandl, Petr (advisor) ; Laušmanová, Monika (referee) ; Keprta, Stanislav (referee)
With the arrival of the New Basel Capital Accord, which was acknowledged by most of Czech banks during the years 2007 and 2008, the importance of internal ratings for the assessment of the health of the whole financial sector has grown tremendously. Internal ratings are now used for the calculation and allocation of capital, as well as for the determination of interest rates and margins. It is the changes of internal ratings which are obvious applications of the multistates models. Through the use of methods usual for the Semimarkovian chains analysis, it is possible to analyze the structure of the internal ratings changes, to monitor the periods between successive changes, and to focus also on the transition matrices themselves. The important part of this work is the comparison of given parameters as observed during steady times, and during the nancial crises, which dates from the fall of the Lehman Brothers in September 2008.


Kapitálový požadavek ke kreditnímu riziku
Burešová, Jana ; Charamza, Pavel (referee) ; Keprta, Stanislav (advisor)
In the present work we study the process of determination of capital requirement for credit risk that is recommended by the Basel Commitee for Banking Supervision to implement into national legislation and that is also obligatory for all European banks since it is a part of the Capital Requirement Directive. At the beginning of this thesis, basic principles and three pillars of The New Basel Capital Accord (2004), better known as Basel II, are described. After focusing on the part of the rst pillar dealing with credit risk, di erent approaches to credit risk measurement are introduced. The most important formula for the advanced internalratings based approach is then analyzed under the settings of mathematical models it is based on. In the last chapter, the output of the formula for capital requirement calculated for a given hypothetic portfolio is compared to the estimate of unexpected loss, that the requirement should correspond to.


Expected Risk of Loan Portfolio
Selementová, Martina ; Herman, Jiří (referee) ; Keprta, Stanislav (advisor)
The rst part of the present work focuses on expected risk of loan portfolio in sense of capital adequacy within IRB approach with accent on input parameters PD, LGD, E and M. We deal with determining of speci c provision to incurred credit loss in compliance with IAS 39 and regarding the analysis of both approaches we show, that in recent conditions speci c provision does not correspond with expected loss as required by Basel II. Next we introduce the internal models for estimating PD, LGD and CF, which are inputs to the calculation of expected loss and partly speci c provision. We discuss the expected loss as a factor determining the nal value of a loan and we show a calculation of risk premium based on the time to default. Last we compare current method for calculation of capital requirement with method based on conditional loss given default.
