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EN
Migration matrices are widely used in risk management. In particular, quality of financial products due to credit risk is described by assigning them to one of several rating categories. The probability of future rating is determined by a migration matrix. Portfolio’s value depends on the rating and on market states. To find an optimal portfolio one should consider migration matrices and the dynamics of market changes. The main goal of our research was to investigate the impact of both risks, market risk and credit risk on portfolio value. On a real portfolio we show that differences in migration matrices that result from the state of economy influence considerably credit risk and portfolio value.
PL
Modele ryzyka kredytowego, używane w bankach, bazują na modelach prawdopodobieństwa zajścia określonych zdarzeń (defaultów). Szeroka klasa tych modeli wykorzystywanych obecnie w praktyce opiera się na estymacji intensywności zdarzeń (ang. intensity-based models). W niniejszej pracy porównujemy wyniki uzyskane przy użyciu modeli Markowa oraz uogólnionych modeli liniowych (GLMM). W pracy przedstawiamy porównanie macierzy migracji w oparciu o różne miary odległości, miary uwzględniające prędkość zbieżności do defaultu oraz miary oparte na teorii absorbujących łańcuchów Markowa. Stosowane miary porównania macierzy migracji odmiennie odzwierciedlają różnice wartości klienta istotne z punktu widzenia biznesu. Modele Markowa dają najlepsze estymatory „biznesowe”, ale są trudne w praktycznych zastosowaniach.
EN
Credit risk models used in banks are based on probability models for occurrence of default. A vast class of these models is based on the notion of intensity In this paper we compare results obtained within Markov chain approach and with help of statistical longitudinal models (GLMM) in which states (rating classes) in discrete time points are regarded as matched pairs. The comparison of obtained migration matrices is based on various distance measures, properties of absorbing Markov chains and convergence to default. Various methods of matrix comparison reflect business based differences between clients in a different way. Markov models give good business estimators but are difficult to apply in practice.
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