We aim to develop an adequate estimation model for loss given default that incorporates the empirically observed bimodality and bounded nature of the distribution. To this end, we introduce an ...adjusted expectation-maximization algorithm to estimate the parameters of a univariate mixture distribution consisting of two beta distributions. Furthermore, we analyze our derived estimation model using estimation models proposed in the literature on synthesized loan portfolios. The simulated loan portfolios consist of possibly loss-influencing parameters that are merged with loss given default observations using 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. PUBLICATION ABSTRACT
Modeling and estimating loss given default (LGD) is necessary for banks that apply for the internal ratings based approach for retail portfolios. To validate LGD estimations, there are only a few ...approaches discussed in the literature. In this paper, two models for validating relative LGD and absolute losses are developed. The validation of relative LGD is important for risk-adjusted credit pricing and interest rate calculations. The validation of absolute losses is important to meet the capital requirements of Basel II. Both models are tested with real data from a bank. Estimations are tested for robustness with in-sample and out-of-sample tests. PUBLICATION ABSTRACT
The intention of a loan loss provision is the anticipation of the loan’s expected losses by adjusting the book value of the loan. Furthermore, this loan loss provision has to be compared to the ...expected loss according to Basel II and, in the case of a difference, liable equity has to be adjusted. This however assumes that the loan loss provision and the expected loss are based on a similar economic rationale, which is only valid conditionally in current loan loss provisioning methods according to IFRS. Therefore, differences between loan loss provisions and expected losses should only result from different approaches regarding the parameter estimation within each model and not due to different assumptions regarding the outcome of the model. The provisioning and accounting model developed in this paper overcomes the before-mentioned shortcomings and is consistent with an economic rationale of expected losses. Additionally, this model is based on a close-to-market valuation of the loan that is in favor of the basic idea of IFRS. Suggestions for changes in current accounting and capital requirement rules are provided.
The intention of a loan loss provision is the anticipation of the loan's expected losses by adjusting the book value of the loan. Furthermore, this loan loss provision has to be compared to the ...expected loss according to Basel II and, in the case of a difference, liable equity has to be adjusted. This however assumes that the loan loss provision and the expected loss are based on a similar economic rationale, which is only valid conditionally in current loan loss provisioning methods according to IFRS. Therefore, differences between loan loss provisions and expected losses should only result from different approaches regarding the parameter estimation within each model and not due to different assumptions regarding the outcome of the model. The provisioning and accounting model developed in this paper overcomes the before-mentioned shortcomings and is consistent with an economic rationale of expected losses. Additionally, this model is based on a close-to-market valuation of the loan that is in favor of the basic idea of IFRS. Suggestions for changes in current accounting and capital requirement rules are provided.
Modeling and estimating the loss given default (LGD) is necessary for banks which apply for the Internal-Ratings Based Approach for retail portfolios. To validate LGD estimations there are only very ...few approaches discussed in the literature. In this paper, two models for validating relative LGDs and absolute losses are developed. The validation of relative LGDs is important for risk-adjusted credit pricing and interest rate calculations. The validation of absolute losses is important to meet the capital requirements of Basel II. Both models are tested with real data of a bank. Estimations are tested for robustness with in-sample and out-of-sample tests.
Modeling and estimating the loss given default (LGD) is necessary for banks which apply for the Internal-Ratings Based Approach for retail portfolios. To validate LGD estimations there are only very ...few approaches discussed in the literature. In this paper, two models for validating relative LGDs and absolute losses are developed. The validation of relative LGDs is important for risk-adjusted credit pricing and interest rate calculations. The validation of absolute losses is important to meet the capital requirements of Basel II. Both models are tested with real data of a bank. Estimations are tested for robustness with in-sample and out-of-sample tests.
Aim of our paper is to analyze the enhancement of portfolio management by using more sophisticated assumptions about distributions and dependencies of stock returns. We assume a skewed t-distribution ...of the returns according to Azzalini and Capitanio (2003) and a dependency structure following a Clayton copula. The risk measure applied to our portfolio selection changed from traditional portfolio variance to downside-oriented conditional value-at-risk. The empirical results show a superior performance of our approach compared to the Markowitz approach and to the approach proposed by Hatherley and Alcock (2007) on a risk-adjusted basis. The approach is applied on daily stock returns of 16 stocks of the EURO STOXX 50.
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 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.
Aim of our paper is to analyze the enhancement of portfolio management by using more sophisticated assumptions about distributions and dependencies of stock returns. We assume a skewed t-distribution ...of the returns according to Azzalini and Capitanio (2003) and a dependency structure following a Clayton copula. The risk measure applied to our portfolio selection changed from traditional portfolio variance to downside-oriented conditional value-at-risk. The empirical results show a superior performance of our approach compared to the Markowitz approach and to the approach proposed by Hatherley and Alcock (2007) on a risk-adjusted basis. The approach is applied on daily stock returns of 16 stocks of the EURO STOXX 50.
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