The aim of our paper is the development of an adequate estimation model for the loss given default, which incorporates the empirically observed bimodality and bounded nature of the distribution. ...Therefore we introduce an adjusted Expectation Maximization algorithm to estimate the parameters of a univariate mixture distribution, consisting of two beta distributions. Subsequently these estimations are compared with the Maximum Likelihood estimators to test the efficiency and accuracy of both algorithms. Furthermore we analyze our derived estimation model with estimation models proposed in the literature on a synthesized loan portfolio. The simulated loan portfolio consists of possibly loss-influencing parameters that are merged with loss given default observations via a quasi-random approach. Our results show that our proposed model exhibits more accurate loss given default estimators than the benchmark models for different simulated data sets comprising obligor-specific parameters with either high predictive power or low predictive power for the loss given default.
Copulas erfreuen sich in der Finanzwirtschaft wachsender Beliebtheit. Ursache hierfür ist insbesondere die Möglichkeit, mit ihrer Hilfe nicht-lineare Abhängigkeitsstrukturen darzustellen. Ein ...weiterer Vorteil besteht darin, dass multivariate Verteilungen mit Hilfe von Copulas separat in ihre Randverteilungen und in ihre Abhängigkeitsstruktur zerlegt werden können. Damit ist die Untersuchung der Abhängigkeitsstruktur losgelöst von Annahmen über die Randverteilungen. Diese Flexibilität ermöglicht die Anwendung von Copulas in zahlreichen Bereichen der Finanzwirtschaft, vom Risikomanagement über die Bewertung von komplexen Finanzprodukten bis zur Portfoliooptimierung. Die vorliegende Arbeit dient zum Einen als didaktischer Einstieg in die Copulathematik und stellt zum Anderen die aktuellen Forschungsergebnisse aus den genannten Bereichen vor.
The intention of a loss provision is the anticipation of credit's expected losses by adjusting the book values of the credits. Furthermore, this loan loss provision has to be compared to the expected ...loss according to Basel II and if necessary, equity has to be adjusted. This however assumes that the loan loss provision and the expected loss are comparable, which is only valid conditionally in current loan loss provisioning methods according to IAS. The provisioning and accounting model developed in this paper overcomes the before mentioned shortcomings and is consistent with an economic rationale of expected losses. We introduce a de¯nition of expected loss referring to the whole maturity of the loan and show that this measure can be reasonably compared with loan loss provisions. Additionally, this model is based on a close-to-market valuation of the loan. Suggestions for changes in current accounting and capital requirement rules are provided.
The intention of a loss provision is the anticipation of credit's expected losses by adjusting the book values of the credits. Furthermore, this loan loss provision has to be compared to the expected ...loss according to Basel II and if necessary, equity has to be adjusted. This however assumes that the loan loss provision and the expected loss are comparable, which is only valid conditionally in current loan loss provisioning methods according to IAS. The provisioning and accounting model developed in this paper overcomes the before mentioned shortcomings and is consistent with an economic rationale of expected losses. We introduce a de¯nition of expected loss referring to the whole maturity of the loan and show that this measure can be reasonably compared with loan loss provisions. Additionally, this model is based on a close-to-market valuation of the loan. Suggestions for changes in current accounting and capital requirement rules are provided.
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. ...Conceptually, DMD performs a low-dimensional spectral decomposition of the data into the following components: The modes, called DMD modes, encode the spatial contribution of the decomposition, whereas the DMD amplitudes specify their impact. Each associated eigenvalue, referred to as DMD eigenvalue, characterizes the frequency and growth rate of the DMD mode. In this paper, we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields. We begin with the theoretical background of DMD and its application to unsteady flow. Next, we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform. Our analysis shows that the current use of DMD components has several drawbacks. To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition: We show that our improved components describe the flow more adequately. Moreover, we remove redundancies in the decomposition and clarify the interplay between components, allowing users to understand the impact of components. These new representations ,which respect the spatio-temporal character of DMD, enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components. With a number of typical examples, we demonstrate that the combination of these techniques allow new insights with DMD for unsteady flow.
