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Markov chains and credit risk theory
Cvrčková, Květa ; Prokešová, Michaela (advisor) ; Lachout, Petr (referee)
Markov chains have been widely used to the credit risk measurement in the last years. Using these chains we can model movements and distribution of clients within rating grades. However, various types of markov chains could be used. The goal of the theses is to present these types together with their advan- tages and disadvantages. We focus our attention primarily on various parameter estimation methods and hypotheses testing about the parameters. The theses should help the reader with a decision, which model of a markov chain and which method of estimation should be used for him observed data. We focus our attention primarily on the following models: a discrete-time markov chain, a continuous-time markov chain (we estimate based on continuous- time observations even discrete-time observations), moreover we present an even- tuality of using semi-markov chains and semiparametric multiplicative hazard model applied on transition intensities. We illustrate the presented methods on simulation experiments and simu- lation studies in the concluding part. Keywords: credit risk, markov chain, estimates in markov chains, probability of default 1
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The impact of the COVID-19 crisis on bank corporate credit risk management in the US and the UK
Kořínek, Matěj ; Teplý, Petr (advisor) ; Kraicová, Lucie (referee)
The thesis deals with bank corporate credit risk management during the COVID-19 crisis in the US and the UK. As a proxy of corporate credit risk, we employ corporate aggregate probability of default provided by Credit Benchmark. To measure the impact of the crisis on corporate aggregate probability of default, we use variables representing macroeconomic and financial market environments. Furthermore, as proxies for the COVID-19 shock and governments' fiscal measures, we employ COVID-19 stringency index and dummy variable(s), respectively. Our data set consists of 60 monthly observations, and by its structure is suitable for time series analysis. The analysis is based on Ordinary Least Squares, Two Stage Least Squares, and Generalized Method of Moments estimations. The results show that fiscal measures "artificially" decreased change of corporate aggregate probability of default in both countries. We recommend that the respective bank credit risk managers incorporate proxies representing fiscal measures in their estimation of through-the-cycle probability of default that serves as an input for calculating regulatory capital. Besides, a variable representing stringency index is found to be significant in the US's model. Thus, we recommend using such a proxy as input for stress testing in the US.
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Nové metody ve schvalování úvěrů
Rychnovský, Michal ; Arlt, Josef (advisor) ; Pecáková, Iva (referee) ; Veselý, Petr (referee)
This thesis contributes to the field of applied statistics and financial modeling by analyzing mathematical models used in retail credit underwriting processes. Specifically, it has three goals. First, the thesis aims to challenge the performance criteria used by established statistical approaches and propose focusing on predictive power instead. Secondly, it compares the analytical leverage of the established and other suggested methods according to the newly proposed criteria. Third, the thesis seeks to develop and specify a new comprehensive profitability-based underwriting model and critically reflect on its strengths and weaknesses. In the first chapter I look into the area of probability of default modeling and argue for comparing the predictive power of the models in time rather than focusing on the random testing sample only, as typically suggested in the scholarly literature. For this purpose I use the concept of survival analysis and the Cox model in particular, and apply it to a real Czech banking data sample alongside the commonly used logistic regression model to compare the results using the Gini coefficient and lift characteristics. The Cox model performs comparably on the randomly chosen validation sample and clearly outperforms the logistic regression approach in the predictive power. In the second chapter, in the area of loss given default modeling I introduce two Cox-based models, and compare their predictive power with the standard approaches using the linear and logistic regression on a real data sample. Based on the modified coefficient of determination, the Cox model shows better predictions. Third chapter focuses on estimating the expected profit as an alternative to the risk estimation itself and building on the probability of default and loss given default models, I construct a comprehensive profitability model for fix-term retail loans underwriting. The model also incorporates various related risk-adjusted revenues and costs, allowing more precise results. Moreover, I propose four measures of profitability, including the risk-adjusted expected internal rate of return and return on equity and simulate the impact of the model on each of the measures. Finally, I discuss some weaknesses of these approaches and solve the problem of finding default or fraud concentrations in the portfolio. For this purpose, I introduce a new statistical measure based on a pre-defined expert critical default rate and compare the GUHA method with the classification tree method on a real data sample. While drawing on the comparison of different methods, this work contributes to the debates about survival analysis models used in financial modeling and profitability models used in credit underwriting.
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The Estimation of Probability of Default Using Logistic Regression
Jiřičko, Pavel ; Dlouhá, Zuzana (advisor) ; Formánek, Tomáš (referee)
The aim of the thesis was to build a probability prediction model for client loan repayment. First, the author selected suitable explanatory variables and explained these in detail in the thesis. The author examined various quantities both for qualitative variables (e.g. failure rates and scores) and quantitative variables (e.g. means and standard deviations) describing individual categories. The predictions were done by the use of logistic regression. The estimated coefficients of individual explanatory variables were examined in terms of their statistical significance. The author also described the impact of individual explanatory variables on the probability of a clients default. The probabilities were calculated for two clients with specific values of explanatory variables. The author managed to build a model that can be used to predict probability of client loan repayment defaults.
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Markov chains and credit risk theory
Cvrčková, Květa ; Prokešová, Michaela (advisor) ; Lachout, Petr (referee)
Markov chains have been widely used to the credit risk measurement in the last years. Using these chains we can model movements and distribution of clients within rating grades. However, various types of markov chains could be used. The goal of the theses is to present these types together with their advan- tages and disadvantages. We focus our attention primarily on various parameter estimation methods and hypotheses testing about the parameters. The theses should help the reader with a decision, which model of a markov chain and which method of estimation should be used for him observed data. We focus our attention primarily on the following models: a discrete-time markov chain, a continuous-time markov chain (we estimate based on continuous- time observations even discrete-time observations), moreover we present an even- tuality of using semi-markov chains and semiparametric multiplicative hazard model applied on transition intensities. We illustrate the presented methods on simulation experiments and simu- lation studies in the concluding part. Keywords: credit risk, markov chain, estimates in markov chains, probability of default 1
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Causes of segregation in microregions
Illmannová, Anne ; Sieber, Martina (advisor) ; Vlček, Josef (referee)
This bachelor thesis concerns the repayment of bank loans. The theoretical part of the thesis deals with the history of banking, its contemporary appearance and sorts of bank financial loan products. Special attention is paid to mortgages and conditions of their acquisition. The practical part of the thesis concerns the confrontation of probability of default in dependence on different indicators on regional and afterwards on district level. The aim of the thesis is to explane on a concrete case from Prague, which sociodemografic characteristics have influence on the payment moral of the debtors, what the differeces are between areas with people who have good and bad payment moral and if the domicile has influence on the level of payment moral. Keywords Banking, mortgage, credit scoring, probability od default.
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The Estimation of Probability of Default Using Logistic Regression
Chalupa, Tomáš ; Dlouhá, Zuzana (advisor) ; Formánek, Tomáš (referee)
The aim of this work is to develop a suitable model that estimates a probability of default of client's loan. As estimation method was used a logistic regression and a probit regression and two definitions of default, 60 and 90 days overdue. The work describes the method of construction, estimation and testing of scoring models and a structure of dataset, which was used in the practical part. Firstly, it was created a theoretical model that was later confronted with estimates. Estimated models were compared by described statistics as McFadden R^2, the ability to diversify was investigated by the Lorenz curve and by the Gini coefficient. It was found that the logistic and the probit regressions have almost the same results, and that 90 days is preferable definition of default than 60 days.
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Basel II. and the calculation of the capital requirement relating to credit risk
Netolická, Klára ; Blahová, Naděžda (advisor)
The bachelor thesis focuses on the calculation of the capital requirement concerning credit risk from the perspective of the Basel II. capital agreement. Firstly, a broader framework is introduced, treating capital adequacy and the preceding concepts that were followed by the Basel II. approaches. Subsequently, the thesis deals with two alternative calculations between which banks can choose -- the standardized approach and the internal ratings based approach, with an emphasis on the latter. The author proceeds from a general formulation of the calculation to its particular elements. Fairly detailed treatment is given to the inference of the risk weight function and to the methods of estimating the probability of default, one of the function's parameters.
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Řízení rizika pohledávek
Hoč, Juraj ; Marek, Petr (advisor) ; Kaiser, Libor (referee)
V mé diplomové práci porovnávám riziko nesplacení pohledávky a náklady jejího zajištění prostřednictvím zajišťovacích instrumentů dostupných na českém trhu a ověřuji, zdali je v daném případě ekonomicky výhodné zajišťovací instrument využít nebo ne. Za pomoci bankrotních modelů a tranzitivních matic ratingových agentur analyzuji pravděpodobnost úpadku firmy do jednoho roku a následně ji promítám do hodnoty pohledávky. Toto riziko kvantifikované přes očekávanou ztrátu porovnávám s náklady na její zajištění u bankovní záruky, dokumentárního akreditivu a faktoringu.
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