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In the last few years we have witnessed growing interest in Dynamic Financial Analysis (DFA) in the nonlife insurance industry. DFA combines many economic and mathematical concepts and methods. It is almost impossible to identify and describe a unique DFA methodology. There are some DFA software products for nonlife companies available in the market, each of them relying on its own approach to DFA. Our goal is to give an introduction into this field by presenting a model framework comprising those components many DFA models have in common. By explicit reference to mathematical language we introduce an up-and-running model that can easily be implemented and adjusted to individual needs. An application of this model is presented as well. [Roger Kaufmann, Andreas Gadmer, Ralf Klett]
9413 Downloads07.12.2006
Datei downloaden Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student's t copula, we ¯nd that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant. [Erik Kole, Kees Koedijk, Marno Verbeek]
10933 Downloads07.12.2006
Datei downloaden We consider "copula skew models" that account for the correlation smile in the pricing of synthetic CDO tranches. These can be viewed as stochastic or local correlation models and are extensions of the well-known one factor Gaussian copula model. We analyse these models through their conditional default probability distributions and marginal compound correlations. We also give some examples of using a particular stochastic correlation model to fit the market, illustrating the stability of the parameters over time.
11911 Downloads07.12.2006
Datei downloaden Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copulabased multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. We apply this idea to the three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle (2002), the varying correlation (VC) model of Tse and Tsui (2002), and the BEKK model of Engle and Kroner (1995). Monte Carlo experiment is conducted to illustrate the performance of C-MGARCH vs MGARCH models. Empirical analysis with a pair of the U.S. equity indices and two pairs of the foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection criteria (likelihood, AIC, SIC) and out-of-sample multivariate density forecast.
7856 Downloads07.12.2006
Datei downloaden Lévy copulas are functions that completely characterize the law of a multidimensional Lévy process given the laws of its components. In this paper, after recalling the basic properties of Levy copulas, we discuss the simulation of multidimensional Lévy processes with dependence structure given by a Lévy copula. Being able to describe the dependence structure of a Lévy process in terms of its Lévy copula allows us to quantify the effect of dependence on the prices of basket options in a multidimensional exponential Lévy model. We conclude that these prices are highly sensitive not only to the linear correlation between assets but also to the exact type of dependence beyond linear correlation.
8669 Downloads07.12.2006
Datei downloaden In this article we focus on the latent variable approach to modelling credit portfolio losses. This methodology underlies all models that descend from Merton's firm-value model (Merton 1974). In particular, it underlies the most important industry models, such as the model proposed by the KMV corporation and CreditMetrics. In these models default of an obligor occurs if a latent variable, often interpreted as the value of the obligor's assets, falls below some threshold, often interpreted as the value of the obligor's liabilities. Dependence between default events is caused by dependence between the latent variables. The correlation matrix of the latent variables is often calibrated by developing factor models that relate changes in asset value to changes in a small number of economic factors. [Rüdiger Frey, Swiss Banking Institute, University of Zurich / Alexander J. McNeil, Department of Mathematics, ETH Zurich / Mark A. Nyfeler, Investment Office RTC, UBS Zurich]
9825 Downloads07.12.2006
Datei downloaden The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively. [Stefano Demarta & Alexander J. McNeil, Department of Mathematics, Federal Institute of Technology, ETH]
10163 Downloads07.12.2006
Datei downloaden Risiko-Management ist seit dem „Gesetz zur Kontrolle und Transparenz im Unternehmensbereich“ (KonTraG) zur unternehmerischen Pflichtaufgabe geworden. Immer anspruchsvollere Methoden werden entwickelt, um interne und externe Gefahren zu erkennen, zu bewerten, zu aggregieren oder zu steuern und zu kontrollieren. Doch selbst wenn es versierten Risiko-Managern gelingt, das Unternehmen gegen Naturkatastrophen, Patentrechtsverletzungen, Datenverlust etc. abzusichern, klafft eine Sicherheitslücke im Risiko-Management, die durch unzureichendes oder falsches Marken-Verständnis zustande kommt. Dabei ist die Marke der Hauptrenditebringer des Unternehmens. So erwirtschaftete der Multimarkenkonzern Unilever mit den stärksten Marken aus seinem Portfolio – nach eigenen Angaben – 85 % der Erlöse und will diesen Anteil in Zukunft noch steigern. Der Schutz dieses wichtigsten Kapitals des Unternehmens, dem bislang noch zu wenig Bedeutung beigemessen wird, sollte integraler Bestandteil eines ganzheitlichen Risiko-Managements werden. [Quelle: Fachbeitrag aus: "Erfolgsfaktor Risikomanagement: Chance für Industrie und Handel" (Frank Romeike und Robert Finke, Gabler Verlag, April 2003)]
10244 Downloads06.12.2006
Datei downloaden Marken generieren Wertschöpfung – so viel ist sicher. Doch eine konsequent markenzentrierte Unternehmensstrategie birgt auch Risiken. Ein proaktives Risikomanagement hilft, Brands richtig vor Einbrüchen und Wertverlusten zu schützen. [Quelle: Acquisa Ausgabe 02/2005, Haufe Fachmedia GmbH & Co. KG, S. 26-28]
9347 Downloads06.12.2006
Datei downloaden Ein Rating soll darüber Auskunft geben, mit welcher Wahrscheinlichkeit Schuldner Zins- und Tilgungszahlen für Kredite leisten werden. Da ein Urteil über die Solvenz von morgen anhand der Bilanz von gestern nur bedingt möglich ist, gewinnen „weiche“ Faktoren und immaterielle Vermögensgegenstände an Bedeutung. Viele Banken berücksichtigen heute schon Einflussgrößen wie die Qualität des Managements und die Flexibilität der Produktionsprozesse. Erstaunlich ist, dass dem wichtigsten Werttreiber von Unternehmen kaum Beachtung geschenkt wird: der Marke.
9381 Downloads06.12.2006
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