Abstracts and Talks
Last update: April 16, 2012.
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Modeling dependent credit rating transitions by coupled Markov chains:
parameters estimation and empirical default correlations
D.V. Boreiko*, Y.M. Kaniovski* and G.Ch.Pflug**
*School of Economics and Management
Free University of Bozen-Bolzano, Bolzano, Italy
**Department of Statistics and Decision Support Systems,
University of Vienna, Vienna, Austria
Maximum likelihood estimates are obtained for the parameters of the coupled Markov chains model by Kaniovski and Pflug (2007) and its modification by Wozabal and Hochreiter (2012). The debtors from a Standard and Poor's data set are classified in two non-default credit classes and 12 industry sectors. The observations cover 30 OECD countries from 1991 through 2006. One-year default correlations are estimated.
Key words: maximum likelihood, dependent credit rating transitions, one-year default correlations, constrained optimization, coupled Markov chains.
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A Dynamic Default Dependence Model
Sara Cecchetti
Economic Outlook and Monetary Policy Department, Bank of Italy, Rome (Italy)
A dynamic multivariate default model is developed. Default times are modelled as random variables with possibly different marginal distributions, and Lévy subordinators are used to model the default times dependence in a portfolio of credit risky assets. In particular a cumulative dynamic hazard process is defined and modelled as a Lévy subordinator, which allows for jumps and induces positive probabilities of joint defaults. The main asset classes in the portfolio are allowed to have different cumulative default probabilities and corresponding different cumulative hazard processes. Under this heterogeneous assumption the portfolio loss distribution is computed in closed form. Using an approximation of the loss distribution, the model is calibrated to the tranches of the iTraxx Europe. Once the multivariate default distribution is estimated, the distress dependence in the portfolio is analyzed by computing indicators of systemic risk as the Stability Index, the Distress Dependence Matrix and the Probability of Cascade Effects.
Joint work with Giovanna Nappo.
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Within and Between Systemic Country Risk: Theory and Evidence from the Sovereign Crisis in Europe
Umberto Cherubini
Dipartimento di Matematica per le Scienze Economiche e Sociali
Università di Bologna, Bologna, Italy
We propose a hierarchical Marshall-Olkin model of countrywide systemic risk. At the lower level, we model the systemic risk of a crisis within the banking system (that we call “within” systemic risk) and at the higher level we model the probability of a joint default of the banking system and the public sector (that we call “between” systemic risk). As for the within systemic risk, we propose a technique, that we call Cuadras-Augé filter, to extract the probability intensity of a systemic event. The filter is used to measure the systemic component of the banking system and to link it, at the higher level, with sovereign risk.
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Vine copulas and their applications
Claudia Czado
Lehrstuhl für Mathematische Statistik
Technische Universität München, Garching-Hochbrück, Germany
In many application one is interested in modeling dependencies among several components. In multivariate problems these dependencies might involve non-symmetric and heavy tail dependencies for different pairs of variables. I will introduce the pair-copula construction of a class of flexible multivariate copulas called vines, which can accommodate this task. These models consist out of a sequence of linked trees, a class of bivariate copulas and their corresponding parameters. I will discuss these models as well as their estimation and model selection. Applications will be in area of financial data.
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TVICA - Time Varying Independent Component Analysis and Its Application to Financial Data
Wolfgang K. Härdle
Ladislaus von Bortkiewicz Chair of Statistics
C.A.S.E. - Center for Applied Statistics & Economics
Humboldt-Universität zu Berlin, Berlin, Germany
Source extraction and dimensionality reduction are important in analyzing high dimensional and complex financial time series that are neither Gaussian distributed nor stationary. Independent component analysis (ICA) method can be used to factorize the data into a linear combination of independent components, so that the high dimensional problem is converted to a set of univariate ones. However conventional ICA methods implicitly assume stationarity or stochastic homogeneity of the analyzed time series, which leads to a low accuracy of estimation in case of a changing stochastic structure. A time varying ICA (TVICA) is proposed here. The key idea is to allow the ICA filter to change over time, and to estimate it in so-called local homogeneous intervals. The question of how to identify these intervals is solved by the LCP (local change point) method. Compared to a static ICA, the dynamic TVICA provides good performance both in simulation and real data analysis. The data example is concerned with independent signal processing and deals with a portfolio of highly traded stocks.
Joint work with Ray-Bing Chen and Ying Chen.
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Contagion in financial networks
Piotr Jaworski
Institute of Mathematics, University of Warsaw, Warszawa, Poland
My talk will deal with application of conditional copulas in modeling of the impact of the close to default state of one financial institution on the welfare of the others.
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A multivariate default model with spread and event risk
Jan-Frederik Mai
Assenagon Credit Management GmbH, München, Germany
On the one hand, daily movements of observable credit spreads contain information about time-varying default probabilities. The standard approach to reproduce these movements is the intensity based ansatz. On the other hand, the fear of cataclysmic events is better captured by a number of (static) copula models. The present paper presents an approach that aims to explain both features, while still being simple enough to allow for non-simulation based pricing routines.
Joint work with P. Olivares, S. Schenk, M. Scherer
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Risk Diversification for Extremal Events
Georg Mainik
Department of Mathematics, ETH Zürich, Switzerland
This talk addresses the problem of portfolio optimization with respect to extremal losses in crisis events. It presents a series of results on portfolio loss asymptotics for multivariate regularly varying random vectors. The examples include elliptical and linear models with heavy-tailed assets.
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Localizing Temperature Risk
Ostap Okhrin
Ladislaus von Bortkiewicz Chair of Statistics
C.A.S.E. - Center for Applied Statistics & Economics
Humboldt-Universität zu Berlin, Berlin, Germany
On the temperature derivative market, modelling temperature volatility is an important issue for pricing and hedging. In order to apply the pricing tools of financial mathematics, one needs to isolate a Gaussian risk factor. A conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation. Empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedasticity with a periodic pattern. The object of this research is to estimate this heteroscedastic function so that, after scale normalisation, a pure standardised Gaussian variable appears. Earlier work investigated this temperature risk in different locations and showed that
neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the volatility process well. Therefore, we consider a local adaptive modelling approach to find, at each time point, an optimal smoothing parameter to locally estimate the seasonality and volatility. Our approach provides a more flexible and accurate fitting procedure for localised temperature risk by achieving nearly normal risk factors. We also employ our model to forecast the temperature in different cities and compare it to a model developed in Diebold and Inoue (2001).
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Sharp bounds on the VaR for sums of dependent risks
Giovanni Puccetti
Dipartimento di Matematica per le Decisioni, Università di Firenze, Italy
We propose a new algorithm to compute numerically sharp lower and upper bounds on the Value-at-Risk for the sum of d dependent random variables having fixed marginal distributions. Compared to the existing literature, the bounds are widely applicable, more accurate and more easily obtained.
Joint work with L. Rüschendorf.