
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.


The Application of the Markov Chains in Credit Risk Models
Bořánek, Jan ; Mandl, Petr (referee) ; Benková, Markéta (advisor)
Credit risk management has become the key instrument for better portfolio diversification and related minimalization of possible loss. Upon the credit risk management we can estimate amount of company's loss brought with creditworthiness of its obligors. Lots of models dealing with credit risk have been developed and most of them are based on Markov Chains theory. This theory also makes up the basis of CreditMetrics, the model which we introduce. Rating migration matrix is the basic input into this model. Two chapters are concerned with constructing and modifying of such matrices. Other chapters deal at firs with general simulation and data analysis on the real credit portfolio come after. CD with input data and computational procedure in Mathematica is also added. The code is pasted as an appendix, too.


Determining the Exposition Measure of the Credit and Market Risk Using the VaR Methods
Friedrichová, Andrea ; Stařík, David (advisor) ; Benková, Markéta (referee)
The thesis examines the share of market and credit exposition on the total rate of risk of an equity index. The paper describes models for estimation of market risk using the ValueatRisk methods, which are the parametric approach, the historical simulation and the Monte Carlo simulation. Further, it describes the estimation of credit risk using the ValueatRisk. The main goal is to descibe and then to adopt in practise three methods for calculating integrated VaR: integrated VaR model based on historical data, integrated VaR with regard to the covariance between market and credit risk and integrated VaR based on the parametric approach to VaR. These methods are applied to selected equities of the index S&P 500 and compared.

 

Actuarial approach to credit risk modelling
Benešová, Milena ; Mandl, Petr (referee) ; Benková, Markéta (advisor)
This thesis deals with one of the models for the credit risk measurement  the model CreditRisk+. The theoretical part describes the theory which is the basis for this model. Further, the thesis demonstrates an applicative example of calculation distribution of default losses. The model uses Poisson distribution as the distribution of the number of defaults from this we can proceed to the distribution of default losses which is output from this model. The theoretical part also presents two variants of this model. The first of this variant is the calculation of the distribution of default losses with fixed default rates. The main asset of this model is the second variant which calculates with the variable default rates. The applied part deals with the recurrence relation which is described with the modelmakers. This thesis deals with the combination of CreditRisk+ with the another model known as CreditMetrics, too. The calculation is realized on the basis of Monte Carlo's simulation of the future portfolio. The aim of this part is to demonstrate how this model is applicable in practise.


Calculation of the Credit Value at Risk
Zamazal, David ; Mandl, Petr (referee) ; Benková, Markéta (advisor)
Thesis describes calculation of the credit value at risk for portfolio composed of traditional bank loans. The risk is measured by incurred expected and unexpected losses at the end of some time horizon. Thesis is splitted into two parts  theoretical part and computational part. The most known and most widely used models are described in the first part, in conjunction with definition of their main input parameters  probability of default, exposure at default, loss given default and correlation between debtors. Detailed theoretical description of two chosen methods comes after  CreditMetrics method and Vasicek's method. The examined portfolio is characterized in the computational part, along with other input parameters, essential for evaluation. Then model implementation into software Mathematica is described, evaluation run and the results. Eventually both methods are compared.


Credit Risk Valuation
Pleška, Martin ; Benková, Markéta (referee) ; Charamza, Pavel (advisor)
According to the rules stated in the Basel II document banks are obliged to calculate risk capital on the basis of expected value of credit risk and in particular on the basis of some of its characteristics among which is Value at Risk (VaR) also ranked. It can be calculated for example by the method stated in Creditmetrics paper. In this thesis we will focus on this method of calculation of VaR which is considered to be a measure of credit risk. Determination of expected value of portfolio which credit risk we are concerned about is in this paper demonstrated by two methods. First one is the method of discounted cash řow and the second one is the method of risk costs. Estimations of VaR are being performed through the use of simulation of distribution of the value of the portfolio. The work is amended by a particular calculation with real data.
