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Invited Talks - Abstracts

 

 

Precise large deviations probabilities for a heavy-tailed random walk

 

Thomas Mikosch, University of Copenhagen; Denmark

   

In this talk we will consider the tail probabilities of partial sum processes for stationary processes whose marginal distribution has power law tails. These results generalize the classical results by A.V. and S.V.

Nagaev who showed that the "heavy-tail heuristics" applies in this case: the power law tails of the partial sums are essentially due to the maximum term in the sum; see Section 8.6 in Embrechts, Klueppelberg and Mikosch (1997).

The situation changes in the case of dependent sequences. Then extremal clusters shape the form of the tails of the partial sums. But in contrast to the tails of the maxima, the extremal index does not appear in these quantities.

In contrast to the tail behavior of partial maxima there are only very few particular cases where we can determine the tail behavior of partial sums for stationary sequences.

We will consider some known cases, compare them with the iid case and indicate how these large deviation results can be used to proved results about ruin probabilities.

 

 

 

 

Extremal dependence of time series

 

Holger Drees, University of Hamburg, Germany

 

 

We consider time series of log returns of a financial investment. In order to assess the risk of extreme losses, it does not suffice to analyze the marginal tail behavior, because the potential total loss is strongly influenced by the clustering behavior of large negative returns on consecutive periods.
We present a systematic approach to the analysis of the extremal serial dependence of such time series using empirical process theory. Particular attention is turned to the bias which is known to often cause serious misjudgment of the clustering behavior. Further potential applications of the theory, e.g. to the discrimination between time series models, are sketched.

 

 

 

Modeling electricity markets: spots, forwards and risk premiums

 

Claudia Klüppelberg, Munich University of Technology, Germany

 

 

We present a new model for the electricity market dynamics, which is able to capture seasonality, low-frequency dynamics and the extreme peaks in the spot price as well as the much less volatile forward prices. We introduce a non-stationary process for trend, seasonality and low-frequency dynamics, and model the large fluctuations by a non-Gaussian stable CARMA process.
We identify all components of our model, in particular, we separate the different components of our model and suggest a robust L1-filter to find the states of the CARMA process. We discuss possibilities for equivalent martingale measures in our heavy-tailed model, which leads to the estimation of the market price of risk and the risk premium in this market.
We apply this procedure to data from the German electricity exchange EEX. For this market we detect a clear negative risk premium, which indicates that the electricity producers are price takers willing to accept a lower price to hedge their production.
This is joint work with Fred Benth and Linda Vos from Oslo University.

 

 

 

Systemic risk in financial system: an extreme value approach

 

Chen Zhou, Central Bank of the Netherlands - De Nederlandsche Bank, Amsterdam, The Netherlands

 

 

The unfolding of the financial crisis since 2008 raises the questioning on the current regulation and supervision of the financial system. In the debate of regulation reform, instead of limiting risk taking of individual financial institution, managing systemic risk is widely agreed as the focus of the new regulation framework, the so-called "macro-prudential" regulation.

We investigate the systemic risk on the cross-sectional dimension: the interconnectedness among financial institutions. This talk departures from comparing a few potential measures on the systemic risk, continues with discussing potential drivers driving the systemic risk, and concludes with policy advices that help manage the systemic risk.

Extreme Value Theory, particularly its multivariate version, is the major tool in both theoretical modeling and empirical assessment within this context.

 

 

 

Risk Measures of Autocorrelated Hedge Fund Returns

 

Casper de Vries, Erasmus University Rotterdam, The Netherlands

 

 

Standard risk metrics tend to underestimate the true risks of hedge funds due to serial correlation in the reported returns. Getmansky, Lo and Makarov (2004) derive mean, variance, Sharpe ratio and beta formulas adjusted for serial correlation. Following their lead, we derive adjusted downside and global measures of univariate and systemic risk. We distinguish between normally and fat tailed distributed returns and show that adjustment is particularly relevant for downside risk measures in the case of fat tails.

A hedge fund case study reveals that the unadjusted risk measures considerably underestimate the true extend of single and multivariate risks.

 

 

 

Mathematical Problems underlying Quantitative Risk Management (QRM)

 

Paul Embrechts, ETH Zurich, Switzerland

 

 

QRM has become an important field of applied mathematical research with considerable impact in such fields as for instance Climate Change, Finance and Insurance.

In this talk I will give examples of mathematical research resulting from QRM related questions.
I will also give an outlook of potentially interesting future fields of methodological research.

 

 

This page was last updated on 10/06/2011

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