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RISK DAY 2006
Mini-Conference on Risk Management in Finance and Insurance
organised by
Location:
ETH Zürich, Main Building, Rämistrasse 101, 8092 Zürich
Lecture Theatre HG F3 ().
Refreshments in the «Uhrenhalle» (main hall, F-floor)
Time:
Friday, October 20, 2006, full day
Conference program:
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8.50–9.00 |
Prof. Dr. Paul Embrechts
(Department of Mathematics,
ETH Zürich)
Opening
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9.00–9.45 |
Prof. Dr. Dilip Madan
(Department of Finance,
Robert H. Smith School of Business,
University of Maryland, USA)
Sato Processes and the Valuation of Structured Products
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Abstract: We report on the adequacy of using Sato processes to
value equity structured products. A pricing comparison of these processes
with other standard models like Heston stochastic volatility,
with and without jumps, VGSA, local volatility and local CGMY are also provided.
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9.45–10.15 |
Johannes Wissel
(Department of Mathematics,
ETH Zürich)
Term structures of implied volatilities: Absence of arbitrage and existence results
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Abstract:
In this talk we study modelling and existence issues for
market models of stochastic implied volatility in a continuous-time
framework with one stock, one bank account and a family of European options
for all maturities with a fixed payoff function h.
We first characterize absence of arbitrage in terms
of drift conditions for the forward implied volatilities
corresponding to a general convex h.
For the resulting infinite system of SDEs for the stock and all the forward implied
volatilities, we then study the question of solvability and provide
sufficient conditions for existence and uniqueness of a solution.
We do this for two examples of h, namely calls with a fixed strike
and a fixed power of the terminal stock price, and we give explicit
examples of volatility coefficients satisfying the required assumptions.
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10.15–10.45 |
Coffee Break (Main Hall, F-Floor, «Uhrenhalle») |
10.45–11.30 |
Prof. Dr. Uwe Schmock
(Institute for Mathematical Methods in Economics,
Vienna University of Technology, Austria)
Modelling and Aggregation of Dependent Credit or Operational Risks
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Abstract: The CreditRisk+ methodology allows for numerous useful
extensions
like dependent risk factors, stochastic losses given default,
and
risk groups with joint defaults and dependent losses, to name
the most important ones. These extensions allow to capture
correlations
between defaults as well as between defaults and losses given
default. Even with these extensions, the distribution of the
portfolio loss can be calculated in an efficient and numerically
stable way. In particular, Monte Carlo simulations and the
corresponding stochastic errors are avoided. Using the credit
portfolio loss distribution, value-at-risk, expected shortfall
and
other coherent risk measures can be calculated; a small
variation
allows to calculate risk contributions of individual obligors.
The methodology has also been successfully applied to the
aggregation of
operational risks. (Joint work with Richard Warnung.)
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11.30–12.00 |
Andrea Macrina
(Department of Mathematics,
King's College London, UK)
Infation-linked Securities in a Stochastic Monetary Economy
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Abstract: We propose a class of continuous-time stochastic models for the pricing
of infation-linked assets using a pricing kernel approach. The nominal and real
pricing kernels, in terms of which the price index can be expressed, are modelled
by introducing a bivariate utility function depending on (a) the aggregate rate of
consumption, and (b) the aggregate rate of real benefit conferred by the money
supply. Consumption and money supply policies are chosen such that the expected
joint utility obtained over a speci¯ed time horizon is maximised subject to a budget
constraint that takes into account the "value" of the benefit of the money supply. For
any choice of the bivariate utility function, the resulting model determines a relation
between the rate of consumption, the price level, and the money supply. The model
also produces explicit expressions for the real and nominal pricing kernels, and hence
establishes a basis for the valuation of infation-linked securities. (Work carried out
in collaboration with L. P. Hughston, King's College London.)
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12.00–13.45 |
Lunch Break
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13.45–14.30 |
Prof. Dr. Christoph Schwab
(Seminar of Applied Mathematics,
Department of Mathematics,
ETH Zürich)
Computational Methods for Levy Models in Finance
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Abstract: We report on our development of deterministic computational techniques
for financial models with jumps.
Such models emerged in the past decade as generalizations
of the Black-Scholes models, starting with the work of Madan and Seneta
in 1990. Our approach is based on Galerkin discretization of the
process' infinitesimal generator resp. Dirichlet form in a multiscale basis.
The methods allow to value single and multiperiod contracts, european,
american or exotic, on single underlyings or baskets.
Before illustrating the techniques by a number of case studies,
among others for Levy copula dependence models, stochastic volatility
models and continuous time GARCH models, we explain the computational
techniques and hint at their mathematical background.
Deterministic computation of certain optimal hedging strategies by these
methods will also be addressed.
Joint work of the CMQF group in the Seminar for Applied Mathematics, ETH.
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14.30–15.00 |
Prof. Dr. Alexander Shapiro
(School of Industrial and System Engineering,
Georgia Tech, USA)
Risk Averse Approach to Multistage Stochastic Programming
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Abstract: In this talk we discuss how coherent
risk measures can be applied to risk averse formulations
of stochastic programming problems in a dynamical setting.
We derive the corresponding dynamic programming equations and study their basic properties.
Finally, we discuss computational complexity of such models.
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15.00–15.30 |
Dr. Ulrich Müller
(Financial and Risk Modeling,
Converium Ltd.)
Bootstrapping the Economy - Generating Consistent Scenarios for Risk Management
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Abstract: The fortune and the risk of almost every business venture depends on the
future course of the economy.
There is a strong demand for economic forecasts and scenarios that can be applied to planning
and risk modeling. A method to simulate the future of the world economy is given.
The economy is represented by key variables such as interest rates (yield curves),
inflation, GDP and equity indices, all of these for several currency zones,
plus the foreign exchange rates between the currencies.
The goal is to generate a set of consistent stochastic scenarios that represent
the space of likely future developments.
While there is an ongoing debate on modeling economic scenarios,
the bootstrapping approach has several advantages.
As a non-parametric method, it resamples past market behaviors
rather than using debatable assumptions on models and parameters.
Empirical distributions (with heavy tails) and dependencies between
economic variables are automatically captured. Historical innovation
vectors (= deviations of actual variable values from their prior market expectations)
are sampled and used for simulated scenarios.
Some variable transformations vouchsafe the arbitrage-free consistency
of the generated scenarios, which is a demanding task for interest rates and their term structure.
While usual yield curves are based on interest rates for different maturity periods,
the bootstrapping method deals with forward interest rates for a series of regular
time intervals in the future. Another transformation makes sure that simulated
forward interest rates stay non-negative and accounts for the asymmetry of interest rate risks.
Several straightforward extensions of the method help to overcome some limitations of
the original bootstrapping method. The limited historical data used for resampling
may not contain extreme innovations, but a well-defined modification makes sure that a
small number of simulated scenarios will behave extremely, leading to a realistic modeling
of risks due to shocks. While the original method disrupts serial dependencies,
an additional GARCH filter re-establishes clusters of volatility. Long-term trends
and long-term mean reversion effects such as purchasing power partity are introduced
as small correction terms in the market expections. Thus the method is suitable for
long-term simulations over many years, as tests and applications have shown.
In the main application, the economic scenario generator produces simulated values
for asset classes such as equities, bonds, mortgage-backed securities, hedge funds
and real estate, for six currency zones: US Dollar, Euro, Yen, Sterling,
Swiss Franc and Australian Dollar. More economic variables and currency zones
can be added due to the modularity and flexibility of the method.
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15.30–16.00 |
Coffee Break (Main Hall, F-Floor, «Uhrenhalle»)
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16.00–16.45 |
Andrew Gallacher and Andrew Smith
(Deloitte Switzerland respectively
Deloitte UK)
Risk Geographies
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Abstract: Financial firms are exposed to many risks,
including asset price movements, credit exposures, changing
actuarial assumptions, policyholder behaviour and operational failures.
Leading banks, insurers, universities and consulting firms have invested in tools for fast and
accurate numerical computation of risk information, clear communication of threats and evaluation
of mitigating strategies.
Risk Geographies is a versatile graphical and analytical toolkit for highlighting
the risks facing an organisation and exploring those combined risk events which are most likely and painful.
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16.45–17.15 |
Philippe Ehlers
(Department of Mathematics,
ETH Zürich)
Dynamic Credit Portfolio Derivatives Pricing
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Abstract: In this paper we present a modelling framework for portfolio
credit risk which incorporates the dependence between risk-free interest-rates and the default loss process.
The innovation in this approach is that -- besides the traditional diffusion-based
covariation between loss intensities and interest-rates -- a direct dependence
between interest-rates and the loss process is allowed, in particular default-free interest-rates
can also depend on the loss history of the credit portfolio. Amongst other things this enables
us to capture the effect that economy-wide default events are likely to have on government bond
markets and/or central banks' interest-rate policies. Similar to Schönbucher (2005), the model
is set up using a set of loss-contingent forward interest-rates $f_n(t,T)$ and loss-contingent
forward credit protection rates $F_n(t,T)$ to parameterize the market prices of default-free
bonds and credit-sensitive assets such as CDOs. We show that (up to weak regularity conditions),
existence of such a parameterization is necessary and sufficient for
the absence of static arbitrage opportunities in the underlying assets.
We also give necessary and sufficient conditions on the dynamics of the
parameterization which ensure absence of \emph{dynamic} arbitrage
opportunities in the model. Similar to the HJM drift restrictions for
default-free interest-rates, these conditions take the form of restrictions
on the drifts of $f_n(t,T)$ and $F_n(t,T)$, together with a set of regularity conditions.
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17.15–18.00 |
Apero (Main Hall, F-Floor, «Uhrenhalle»)
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Print version:
download .pdf
General Information
Participation is free, and there is no official registration.
Everyone is welcome, practitioners are especially encouraged to attend.
We have not made any special arrangements for lunch since there are
sufficient possibilities nearby, in particular at
ETH and
the University.
There is also the Dozentenfoyer.
For hotel accommodation, please check the
Zürich Tourism home page.
Organizers:
Conference Secretary:
Ms. Galit Shoham,
HG G21.3 (IFOR),
Phone 044/632 40 16,
E-mail: sekretariat@ifor.math.ethz.ch
Previous Risk Days:
1998, 1999,
2000, 2001,
2002, 2003,
2004,
2005
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