
Precise large deviations
probabilities for a heavytailed 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 "heavytail 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, lowfrequency dynamics
and the extreme peaks in the spot price as well as the much
less volatile forward prices. We introduce a nonstationary
process for trend, seasonality and lowfrequency dynamics,
and model the large fluctuations by a nonGaussian stable
CARMA process.
We identify all components of our model, in particular, we
separate the different components of our model and suggest a
robust L_{1}filter to find the states of the CARMA process.
We discuss possibilities for equivalent martingale measures
in our heavytailed 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 socalled "macroprudential"
regulation.
We
investigate the systemic risk on the crosssectional
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. 



