Credit risk models used in banks are based on probability models for occurrence of default. A vast class of the models used in practice (e.g., Credit Metrics) is based on the notion of intensity. In 1997 Jarrow applied Markov chain approach to analyze intensities. The key problem that arises is the selection of appropriate estimators. Within the Markov approach among the most frequently used estimators of a migration matrix are cohort and duration estimators. Migration matrices can also be obtained with help of statistical longitudinal models (GLMM) in which states (rating classes) in discrete time points are regarded as matched pairs. In this paper we compare Markov chain models and GLMM models and the influence of their application on bank portfolio evaluation.
Simple model of share price evolution, which is an extension of Kehr-Kutner-Binder one and Montero-Masoliver models, is presented. The market empirical data inspired the assumptions of the model. The model seems to be the reference one for the study of the short-range correlations in financial data as it considers the observed correlation over two successive jumps of the financial ant.
In this work we empirically verify the generic breaking of the Central Limit Theorem on the financial and commodity markets. We analysed the distributions of log-returns for typical indices and price of gold, for increasing time horizons. We considered Random Coarse Graining Transformation of the Continuous-Time Random Walk model, which can represent the non-Gaussian price dynamics of underlying assets and the corresponding derivatives, e.g., various options or future contracts. We confirmed that empirical data and predictions of the model quite well agree.
We study crash dynamics of the Warsaw Stock Exchange by using minimal spanning tree networks. We identify the transition of the complex network during its evolution from a (hierarchical) power law minimal spanning tree network - representing the stable state of Warsaw Stock Exchange before the recent worldwide financial crash, to a superstar-like (or superhub) minimal spanning tree network of the market decorated by a hierarchy of trees - an unstable, intermediate market state. Subsequently, we observe a transition from this complex tree to the topology of the (hierarchical) power law minimal spanning tree network decorated by several star-like trees or hubs - this structure and topology represent the Warsaw Stock Exchange after the worldwide financial crash, and can be considered to be an aftershock. Our results can serve as an empirical foundation for a future theory of dynamic structural and topological phase transitions on financial markets.
Predictions for the transmission of genetic traits along to generations are an important process for patients, their family and genetic counseling. For this purpose, Bayesian analysis in which one can include a priori knowledge taking into account all relevant information into the problem could be a useful tool to examine how disease forecasting affects its probability so that it provides a more straightforward interpretation of predictions. Therefore, we investigate here transmissions of autosomal recessive diseases along to generations within Bayesian framework. In order to do that we develop a computer code that is useful to facilitate genetic transition matrices to forecast predictions of probabilities of transmission of genetic traits by using Mathematica software, well known as an algebraic manipulation language. Furthermore, the symbolic implementation of the code is applied for the cystic fibrosis disease forecasting in humans genetics. All results show that Bayesian analysis plays a central role of prediction for probabilities of transmissions of genetic traits along generations for cystic fibrosis disease or other autosomal recessive disorders.
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