Risk Day 2001
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Mini-Conference on Risk Management in Finance and Insurance
organised by RiskLab, ETH Zurich.
Printable and online program with links:
http://www.math.ethz.ch/finance/Risk-Day-2001.html
Time: Friday, October 19, 2001, 9.00 - 17.30
Location: ETH Zurich, Main Building, Lecture Hall HG F7; Refreshments
in the "Uhrenhalle" (main hall, F-floor)
General Information: Participation is free, and there is no official
registration. Everyone is welcome, practitioners are especially
encouraged to attend.
Program:
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9.00 - 9.10
Prof. Dr. Hans-Jakob Lüthi (IFOR and RiskLab, ETH Zürich)
"Welcome and Presentation of RiskLab"
9.10 - 9.50
PD Dr. Wolfgang Breymann (RiskLab, Dept. of Math., ETH Zürich)
"Volatility Estimation and Risk Measurement:
From Short to Long Time Horizons"
Abstract: Market risk management, portfolio optimization and option
pricing methods can only be as good as the model of the underlying
volatility process. An approach will be presented that uses intraday
high-frequency financial data to improve risk measurement at long
time horizons. It takes advantage of the fact that volatility
estimation on a time horizon of the order of days can be improved by
the use of intra-day data. Such data require special methods for data
analysis. The following results will be presented:
- Universal method for deseasonalization of financial time series.
- Use of intra-day data to improve volatility estimates
at daily or longer time horizons.
- Modelling financial time series by means of a hierarchical
volatility model containing a cascade from long to short time
horizons.
An outlook will be given on how to use these techniques for portfolio
optimisation and risk management at longer time horizons.
9.50 - 10.30
Enrico De Giorgi (RiskLab, Dept. of Math., ETH Zürich)
"An Intensity Based Non-Parametric Default Model for Residential
Mortgage Portfolios"
Abstract: In December 2000 Swiss banks held about 505 billion CHF
debts in the form of mortgages. Nonetheless, current models for
credit risk are not designed to capture the specific dependence
characteristics of a large mortgage portfolio. Given the huge size of
the mortgage market, it is surprising that the issue has been largely
ignored by academic research. Our attention lies in a proper way of
modeling default risk for individual residential mortgages, which is
affected by macro-economic factors such as unemployment, mortgage and
factors specific to the obligor. We consider the time to default,
using a non-parametric proportional hazard model for the intensity
process, which is assumed to depend on a set of factors
(macro-economic, mortgage and obligor specific). A technique from
generalized additive models is used for estimation and the
contribution of each factor to the default intensity is computed.
10.30 - 11.00 Coffee Break (Main Hall, F-Floor, Uhrenhalle)
11.00 - 11.30
Filip Lindskog (RiskLab, Dept. of Math., ETH Zürich)
"Multivariate Extremes, Aggregation and Dependence in Elliptical Distributions"
Abstract: The class of elliptical distributions provides a rich
source of multivariate distributions which share many of the
tractable properties of the multivariate normal distribution and
enables modelling of multivariate extremes and other forms of
non-normal dependences. In this talk I aim to clarify dependence
properties of elliptical distributions and give examples how these
results can be applied. (Joint work with Henrik Hult.)
11.30 - 12.00
Alessandro Juri (Dept. of Math., ETH Zürich)
"Using Copulae to Bound the Value-at-Risk for Functions of Dependent Risks"
Abstract: The theory of copulae is known to provide a useful tool for
modelling dependence in integrated risk management. For given risks
X_1,...,X_n and a real-valued functional f on R^n, bounds for the
Value-at-Risk of the global position f(X_1,...,X_n) are provided. The
key point is that we do not have specific dependence information on
X_1,...,X_n. A further issue is how these bounds change when specific
dependence information is assumed. Various examples highlight the
methodology introduced. (Joint work with Andrea Höing and Prof. P.
Embrechts.)
12.00 - 13.40 Lunch Break
13.40 - 14.10
Pierre Patie (RiskLab, Dept. of Math., ETH Zürich)
"Risk Management for Derivatives in Illiquid Markets"
Abstract: In this talk, we study the hedging of derivatives in
illiquid markets. We consider a model where the implementation of a
hedging strategy affects the price of the underlying security. We
derive a formula for the feedback effect of dynamic hedging on market
volatility and characterize perfect hedging strategies by a nonlinear
version of the Black-Scholes PDE. Then we extend our approach to
portfolios of derivatives by providing a pricing rule for the
individual claims in a portfolio assuming that we know the overall
hedge cost and the replicating strategy for the large trader. We
solve numerically the PDE and we provide results (option prices and
greeks) for different kinds of options. On the topic of risk
management, we suggest a methodology to measure liquidity based on
the estimation of implied parameters obtained from real option
prices. Finally, simulations are used to assess the performance of
various hedging strategies under market illiquidity. (Joint work with
Prof. Rüdiger Frey, ISB, University of Zurich.)
14.10 - 14.40
Dr. Jesper Lund Pedersen (RiskLab, Dept. of Math., ETH Zürich)
"An Optimal Selling Strategy Based on Predicting the Ultimate Maximum Price"
Abstract: In this talk I will present an optimal selling strategy for
an asset in the following sense: An investor with a long position in
one asset decides to close the position before a given time. The
investor continuously observes the asset price performance and has to
determine the point in time (selling strategy) to close out the
position so that the asset price is as close as possible to the
ultimate maximum price over the given period. The probable proximity
is measured by a probability distance. Thus, the investor's objective
is to maximize, over all strategies, the probability that the asset
price when the position is closed out is greater than a given
percentage of the ultimate maximum price.
14.40 - 15.10
Dr. Larbi Alili (Dept. of Math., ETH Zürich)
"Exponential Functionals of Brownian Motion and Asian Options"
Abstract: Exponential functionals of Brownian motion play an
important role in the valuation and hedging of Asian options. The aim
of this talk is to provide an elementary method for computing the
distribution of the latter functionals.
15.10 - 15.50 Coffee Break (Main Hall, F-Floor, Uhrenhalle)
15.50 - 16.20
Dr. Dirk Tasche (RiskLab, Dept. of Math., ETH Zürich)
"Expected Shortfall and Beyond"
Abstract: Expected Shortfall (ES) in several variants has been
proposed as a remedy for the deficiencies of Value-at-Risk (VaR),
which in general is not a coherent risk measure. In fact, most
definitions of ES lead to the same results when applied to continuous
loss distributions. Differences may appear when the underlying loss
distributions have discontinuities. In this case even the coherence
property of ES can be lost. The relations between some of the
definitions of ES will be discussed. It will be pointed out that
there is one which is robust in the sense of yielding a coherent risk
measure regardless of the underlying distributions. In contrast to
VaR, this variant of ES can always be estimated naively. Moreover, as
shown recently by S. Kusuoka, it generates in a certain sense the
class of all law invariant coherent risk measures.
16.20 - 16:50
Prof. Dr. Philippe Artzner (RiskLab and Université Louis Pasteur)
"Coherent Acceptability for Multiperiod Risk and Applications"
Abstract: We explain why and how to deal with the definition, the
acceptability and the management of risk in a genuinely multitemporal
way. Acceptable value processes are primitive objects and the measure
of risk of a value process is the initial extra capital which makes
it acceptable. Coherence axioms then provide a representation of a
risk-adjusted valuation as the minimum expected value of an Stieltjes
integral with respect to random measures. Some special cases allowing
for recursive computations are presented. (Joint work with Freddy
Delbaen, Jean-Marc Eber, David Heath and Hyejin Ku.)
17.00 Awarding of the Prize of the Dimitris N. Chorafas Foundation.
Conference Secretary: Mrs G. Baltes, HG G37.2, Phone 01/632 34 00,
E-mail: baltes(a)math.ethz.ch
With best regards,
Uwe Schmock
Home Page:
http://www.math.ethz.ch/~schmock/
Financial and Insurance Mathematics:
http://www.math.ethz.ch/finance/
RiskLab:
http://www.risklab.ch/