An Alternative Maximum Entropy Model for Time-Varying Moments with Application to Financial Returns - Fischer, Matthias; Herrmann, Klaus (Studies in Nonlinear Dynamics and Econometrics, 2010)
With their article on Maximum Entropy (ME) densities for time-varying moments, Rockinger and Jondeau (2002) set a milestone for the application of information theoretic principles to the analysis of financial market data. In this note we briefly discuss the application of their approach to financial data, point out some shortcomings that it encounters and show how these can be overcome. Applying our model to different market indices, we find evidence for time-variability of skewness and kurtosis. Copyright © 2010 The Berkeley Electronic Press. All rights reserve
WiSo-Import:2015-03-26:1146
Keywords: Entropy density; GARCH; Kurtosis; Skewness

An analytic approach to quantify the sensitivity of CreditRisk+ with respect to its underlying assumptions - Fischer, Matthias; Kaufmann, Florian (Journal of Risk Model Validation, 2014)
WiSo-Import:2015-03-26:5276

An empirical analysis of multivariate copula models - Fischer, Matthias; Köck, Christian; Weigert, Florian; Schlüter, Stephan (Quantitative Finance, 2009)
WiSo-Import:2015-03-26:1215

A new class of copulas with tail dependence - Fischer, Matthias; Hinzmann, Gerd (South African Statistical Journal, 2014)
Copula-based multivariate models allow to specify the marginal distributions separately from the dependence structure (i.e. the copula) which links these distributions to form a joint distribution. Within this work we introduce a new family of copulas (™generalized mean copulas™) which is positive comprehensive (i.e. includes both independence and maximum dependence) and allows for upper tail dependence. It includes the Spearman copula and a specific Fréchet copula as special cases. Some properties of the new copula are derive
WiSo-Import:2015-03-26:5275
Keywords: Arithmetic mean; Geometric mean; Tail dependence

An Extended Likelihood Framework for Modeling Discretely Observed Credit Rating Transitions - Pfeuffer, Marius; Möstel, Linda; Fischer, Matthias (Quantitative Finance, 2018)

A Note on a Non-Parametric Tail Dependence Estimator - Fischer, Matthias; Dörflinger, Marco (Far East Journal of Theoretical Statistics, 2010)
WiSo-Import:2015-03-26:1218

A Note on the Kurtosis Ordering of the Generalized Secant Hyperbolic Distribution - Klein, Ingo; Fischer, Matthias (Communications in Statistics-Theory and Methods, 2008)
Two major generalizations of the hyperbolic secant distribution have been proposed in the statistical literature which both introduce an additional parameter that governs the kurtosis of the generalized distribution. The generalized hyperbolic secant (GHS) distribution was introduced by Harkness and Harkness (1968) who considered the pth convolution of a hyperbolic secant distribution. Another generalization, the so-called generalized secant hyperbolic (GSH) distribution, was recently suggested by Vaughan (2002). In contrast to the GHS distribution, the cumulative and inverse cumulative distribution function of the GSH distribution are available in closed-form expressions. We use this property to prove that the additional shape parameter of the GSH distribution is actually a kurtosis parameter in the sense of van Zwet (1964
WiSo-Import:2015-03-26:995
Keywords: Hyperbolic secant distribution; Kurtosis ordering

Application of Vine Copulas to Credit Portfolio Risk Modeling - Fischer, Matthias; Geidosch, Marco (Journal of Financial Risk Management, 2016)
Keywords: pair-copula constructions; vine copulas; Archimedean and elliptical copulas; credit portfolio risk; economic capital; R-vine; D-vine

A primer on multivariate copula models - Fischer, Matthias (Vine Copulas Handbook, 2009)
WiSo-Import:2015-04-20:1222

A Skew Generalized Secant Hyperbolic Family - Fischer, Matthias (Austrian Journal of Statistics, 2006)
WiSo-Import:2015-03-26:1209

A Statistical Repertoire for Quantitative LGD Validation: Overview, Illustration, Pitfalls, Extensions - Fischer, Matthias; Pfeuffer, Marius (Journal of Risk Model Validation, 2014)

A Tail Quantile Approximation formula for the Student t distribution - Fischer, Matthias; Schlüter, Stephan (Communications in Statistics-Theory and Methods, 2012)
WiSo-Import:2015-03-26:4697

Composite Tukey-type distributions with application to operational risk management - Möstel, Linda; Fischer, Matthias; Pfeuffer, Marius (Journal of Operational Risk, 2024)
Similarly to many other quantitative disciplines, operational risk modeling requires flexible distributions defined for non-negative values, which enable heavy-tail behavior. Because they can account for the different requirements related to “extreme” observations in the tail and “ordinary” observations in the body of such distributions, so-called composite or spliced models have gained increasing attention in recent years. The focus of this paper is on composite Tukey-type distributions. This term describes a class of distributions whose tails follow a generalized truncated Tukey-type distribution, which allows for greater flexibility than the commonly used generalized Pareto distribution. After reviewing the classical Tukey-type family, we discuss the leptokurtic properties that emerge from a general kurtosis transformation, and we study several estimation methods for the truncated Tukey-type distribution. Finally, we empirically demonstrate the flexibility of our new composite model with an operational risk data set and business interruption losses.
CRIS-Team Scopus Importer:2024-03-29
Keywords: composite distributions; kurtosis; loss data; skewness; spliced distributions; Tukey-type distributions

Connecting Rating Migration Matrices and the Business Cycle By Means of Generalized Regression Models - Fischer, Matthias; Pfeuffer, Marius (Applied Stochastic Models in Business and Industry, 2016)

Constructing and generalizing given multivariate copulas: A unifying approach - Fischer, Matthias; Köck, Christian (Statistics, 2012)
Recently, Liebscher [Construction of asymetric multivariate copulas, J. Multivariate Anal. 99 (2008), pp. 2234-2250] introduced a general construction scheme of d-variate copulas which generalizes the Archimedean family. Similarly, Morillas [A method to obtain new copulas from a given one, Metrika 61 (2005), pp. 169-184] proposed a method to obtain a variety of new copulas from a given d-copula. Both approaches coincide only for the particular subclass of Archimedean copulas. Within this work, we present a unifying framework which includes both Liebscher and Morillas copulas as special cases. Above that, more general copulas may be constructed. First examples are given. © 2012 Taylor and Francis Group, LL
WiSo-Import:2015-03-26:1216
Keywords: construction of copulas; generalized Archimedean copulas

Construction of Symmetric Generalized FGM Copulas by means of certain Univariate Distributions - Fischer, Matthias; Klein, Ingo (Metrika, 2007)
WiSo-Import:2015-03-26:994

Fast approximation methods for credit portfolio risk calculations - Jakob, Kevin; Churt, Johannes; Fischer, Matthias; Nolte, Kim; Okhrin, Yarema; Sondermann, Dirk; Wilke, Stefan; Worbs, Thomas (Digital Finance, 2023)
Credit risk is one of the main risks financial institutions are exposed to. Within the last two decades, simulation-based credit portfolio models became extremely popular and replaced closed-form analytical ones as computers became more powerful. However, especially for non-homogenous and non-granular portfolios, a full simulation of a credit portfolio model is still time consuming, which can be disadvantageous within some use cases like credit pricing or within stress testing situations where results must be available very quickly. For this purpose, we investigate if methods based on artificial intelligence (AI) can be helpful to approximate a credit portfolio model. We compare the performance of AI-based methods within three different use cases with suitable non AI-based regression methods. As a result, we see that AI-based methods can generally capture portfolio characteristics and speed-up calculations but - depending on the specific use case and the availability of training data - they are not necessarily always the best choice. Particularly, considering the time and costs for collecting data and training of the complex algorithms, non-AI-based methods can be as good as or even better than AI-based ones, while requiring less computational effort.
CRIS-Team Scopus Importer:2024-12-16
Keywords: AI; Approximation; C63; Credit portfolio model; Credit risk; G32

Financial return distributions - Fischer, Matthias (International Encyclopedia of Statistical Sciences, 2009)
WiSo-Import:2015-04-20:1223

Generalized hyperbolic distributions - Fischer, Matthias (International Encyclopedia of Statistical Sciences, 2009)
WiSo-Import:2015-04-20:1220

Generalized Tukey-type distribution with application to financial and teletraffic data - Fischer, Matthias (Statistical Papers, 2010)
WiSo-Import:2015-03-26:1214

gh-transformed of symmetrical distributions - Klein, Ingo; Fischer, Matthias (Contributions to modern econometrics, 2002)

Hyperbolic secant distributions and generalizations - Fischer, Matthias (International Encyclopedia of Statistical Sciences, 2009)
WiSo-Import:2015-04-20:1221

IFRS 9 Impairment von Finanzinstrumenten: Parametrische Modellierung von PD-Kurven - Fischer, Matthias; Pfeuffer, Marius (Risiko Manager, 2016)

Kurtosis modelling by means of the J-transformation - Klein, Ingo; Fischer, Matthias (Allgemeines Statistisches Archiv, 2004)
WiSo-Import:2015-03-26:970
Keywords: Kurtosis - variable transformation - normal transformation - tail elongation

Modeling sector correlation with CR+ - The CBV model. - Fischer, Matthias; Dietz, Christian (Journal of Credit Risk, 2012)
WiSo-Import:2015-03-26:3082

Parameter estimation, bias correction and uncertainty quantification in the Vasicek credit portfolio model - Pfeuffer, Marius; Nagl, Maximilian; Fischer, Matthias; Rösch, Daniel (The Journal of Risk, 2020)
This paper is devoted to the parameterization of correlations in the Vasicek credit portfolio model. First, we analytically approximate standard errors for value-at-risk and expected shortfall based on the standard errors of intra-cohort correlations. Second, we introduce a novel copula-based maximum likelihood estimator for inter-cohort correlations and derive an analytical expression of the standard errors. Our new approach enhances current methods in terms of both computing time and, most importantly, direct uncertainty quantification. Both contributions can be used to quantify a margin of conservatism, which is required by regulators. Third, we illustrate powerful procedures that reduce the well-known bias of current estimators, showing their favorable properties. Further, an open-source implementation of all estimators in the novel R package AssetCorr is provided and selected estimators are applied to Moody’s Default & Recovery Database.
CRIS-Team Scopus Importer:2020-05-19
Keywords: Asset correlation; Bias correction; Copula; Delta method; Margin of conservatism; Vasicek model

Parameter estimation of Tukey-type distributions: A comparative analysis - Möstel, Linda; Fischer, Matthias; Pfaelzner, Fabian; Pfeuffer, Marius (Communications in Statistics-Simulation and Computation, 2019)
Tukey-type distributions (a generalization of Tukey's gh(normal)-distribution) are attractive for a broad spectrum of applications since they can explicitly model flexible skewness and kurtosis features of practical data. However, since the likelihood function is not available in closed-form, the derivation of an accurate estimation method plays a crucial role and henceforth various procedures to overcome this issue were introduced, especially for Tukey's gh(normal)-distribution. After extending these approaches to all Tukey-type distributions, our main contribution is to provide a comprehensive simulation study to compare the methods against each other. Moreover, we illustrate the practical usage for the Nikkei225 stock index data.
CRIS-Team WoS Importer:2019-05-09

Power Kurtosis Transformations: De finitions, Properties and Ordering - Klein, Ingo; Fischer, Matthias (Advances in Statistical Analysis, 2006)
WiSo-Import:2015-03-26:974

pTAS Distributions with Application to Risk Management - Fischer, Matthias; Jakob, Kevin (Journal of Statistical Distributions and Applications, 2016)

Quantifying model risk within a CreditRisk+ framework - Fischer, Matthias; Mertl, Alexander (Journal of Risk Model Validation, 2012)
WiSo-Import:2015-03-26:4730

Quantifying the impact of different copulas in a generalized CreditRisk+ framework - An empirical study - Fischer, Matthias; Jakob, Kevin (Dependence Modeling, 2014)
WiSo-Import:2015-03-26:5332

Skew Generalized Secant Hyperbolic Distributions: Unconditional and Conditional Fit to Asset Returns - Fischer, Matthias (Austrian Journal of Statistics, 2004)
WiSo-Import:2015-03-26:1206

Skewness by Splitting the scale parameter - Klein, Ingo; Fischer, Matthias (Communications in Statistics-Theory and Methods, 2006)
There are several possibilities for introducing skewness into a symmetric distribution. One of these procedures applies two different parameters of scale - with possibly different weights - to the positive and the negative part of a symmetric density. Within this work we show that this technique incorporates a well-defined parameter of skewness, i.e., that the generated distributions are skewed to the right (left) if the parameter of skewness takes values less (greater) than one. Second, we prove that the skewness parameter is compatible with the skewness ordering of van Zwet (1964), which is the strongest ordering in the hierarchy of orderings discussed by Oja (1981). Hence the generated (skewed) distributions can be ordered by the skewness paramete
WiSo-Import:2015-03-26:991
Keywords: Score function; Skewness; Skewness ordering; Skewness to the right

Specifcation risk and calibration effects of a multi-factor portfolio model - Fischer, Matthias; Dorfleitner, Gregor; Geidosch, Marco (Journal of Fixed Income, 2012)
WiSo-Import:2015-03-26:4008

Stress Testing German Industry Sectors: Results from a Vine Copula Based Quantile Regression. - Fischer, Matthias; Kraus, Daniel; Pfeuffer, Marius; Czado, Claudia (Risks, 2017)

Stresstesting und Risikokonzentrationen - Fischer, Matthias; et al. (Jahrbuch Treasury and Private Banking, 2011)
WiSo-Import:2015-04-20:3059

Symmetrical gh-transformed distributions - Klein, Ingo; Fischer, Matthias (Contributions to Modern Econometrics, 2002)

Tailabhängigkeit und Asymmetrie in multivariaten Finanzmarktdaten - Klein, Ingo; Fischer, Matthias (Finanzintermediation: Theoretische, wirtschaftspolitische und praktische Aspekte aktueller Entwicklungen im Bank- und Börsenwesen. Festschrift für Wolfgang Gehrke zum 60. Geburtstag, 2004)
WiSo-Import:2015-04-20:971

The Beta-hyperbolic secant (BHS) distribution - Fischer, Matthias; Vaughan, David (Austrian Journal of Statistics, 2010)
WiSo-Import:2015-03-26:1219

The HS-SAS and GSH-SAS Distribution as Model for Unconditional and Conditional Return Distributions - Fischer, Matthias; Herrmann, Klaus (Austrian Journal of Statistics, 2013)
WiSo-Import:2015-03-26:4699

The weak tail dependence coefficient of the GH distribution - Schlüter, Stephan; Fischer, Matthias (Extremes, 2012)
WiSo-Import:2015-03-26:1759

Tukey-type Distributions in the context of financial data - Fischer, Matthias; Klein, Ingo; Horn, Armin (Communications in Statistics-Theory and Methods, 2007)
Using the Gaussian distribution as probabilistic model for (leptokurtic) financial data is widespread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation (H-transformation) of the standard normal distribution or, more generally, of a symmetric "parent" distribution Z and allow for leptokurtosis represented by the (elongation) parameter H > 0. Alternatively, the J-distributions of Fischer and Klein (2004) or the K-distributions of Haynes et al. (1997) may be applied. In order to additionally introduce skewness, some have these distribution families have been generalized subsequently. Within this work we "complete" the class of so-called Tukey-type distributions by introducing KQ- and JQ-distributions, on the one side, and KK-, JJ-, and [image omitted]-distributions, on the other side. Moreover, we investigate the goodness-of-fit of such Tukey-type distributions for different parent distributions Z in the context of financial return data. In particular, the interplay between Z and different transformations is focussed. Finally, our results are compared to those of popular multi-parametric distribution model
WiSo-Import:2015-03-26:993
Keywords: Financial return data; Kurtosis; Normal transformation; Skewness; Variable transformation

Weighted Power Mean Copulas: Theory and Application - Klein, Ingo; Fischer, Matthias; Pleier, Thomas (Model Assisted Statistics and Applications, 2018)

wHS-type distributions with application to Finance - Fischer, Matthias; Hui, Alexander; Hösle, Stefan (Journal of Statistics and Management Systems, 2017)
Keywords: Hyperbolic secant distribution; Financial returns; Distortion function