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Derivatives and Risk Management in Theory and Practice
1st-2nd April 2004
Dr Ralph Bilger, d-fine
Slides
Ralph Bilger is a senior consultant at d-fine GmbH, and a lecturer in physics
and mathematical finance in the physics department at Tübingen University.
Before joining d-fine, Ralph was working as a consultant for the
Financial and Commodity Risk Consulting group of Andersen, Eschborn, as a financial
engineer for LBBW, Stuttgart and as an assistant professor for Tübingen University.
Ralph holds a Masters degree from the State University of New York, Stony Brook,
a Ph.D. and a Habilitation in particle physics from Tübingen University.
Abstract
Valuation of American-Asian Options with the Longstaff-Schwartz Algorithm
The Least-Squares Monte Carlo (LSM) algorithm of Longstaff & Schwartz is a
new and powerful approach for the valuation of the price of American options. This
approach can also be applied to exotic, path-dependent options where the payoff
and the value of the option depends on the value of the underlying, averaged over a
given time-window (Asian options). So far, only American-Asian options have been
considered where the starting point of the time window used for averaging is fixed.
American-Asian options with rolling time-window, i.e. a time window of constant
width are particularly complex since they constitute a non-Markovian problem, that
can not be transformed to a problem with a finite number of state variables.
In this work, the LSM algorithm is applied to American-Asian options with rolling
time window. The value of the option is determined. The convergence of the algorithm
is studied in dependence of the maximum degree of the polynomials used in the
regression and the number of base variables.
Dr Andreas Binder, MathConsult, Linz
Slides
Andreas Binder is CEO of MathConsult GmbH and of the Industrial Mathematics
Competence Center, Linz. Andreas holds a Ph.D. in Industrial Mathematics
from Linz. After a research period at the Oxford Centre for Industrial and
Applied Mathematics, he became assistant professor at the University of
Linz, until 1996, when he joined MathConsult. His research activities
include numerical analysis of partial differential equations and stable
techniques for paramater identification. Together with his group, he has
been working on computational finance since 1997. In 2001, MathConsult
released the UnRisk PRICING ENGINE, a package for the pricing of complex
structured instruments. Andreas is member of the advisory board of the
Austrian Mathematical Society.
Abstract
Accuracy does matter: High-End Numerical Techniques for the Robust Pricing of Structured Financial Instruments
Many partial differential equations which arise in pricing of financial
instruments under, say, short rate models, are, to speak in the language of
engineers, reaction-convection-diffusion equations. In the one-dimensional
case, it turns out that combining symbolic techniques (Greens?s functions)
and high order numerical integrations schemes delivers very accurate results
also in cases where binomial trees fail. In the higher dimensional case,
computational fluid dynamics has proven that finite element methods combined
with streamline diffusion techniques are robust schemes for the treatment of
these equations. We present the ideas behind these advanced numerical
techniques.
Parameter calibration in interest rate models is a notorious instable
problem. We present the reason behind this phenomenon, and how
regularization techniques should be applied to stabilize the problem.
This is joint work with MathConsult?s Computational Finance Group. Part of
the work has been supported by the Austrian Science Foundation (Project E67:
"Fast Numerical Methods for Computational Finance").
Dr Damir Filipovic, ETH Zurich
Slides
Damir Filipovic works in the research and development group at the Swiss
Federal Office of Private Insurance (FOPI). He develops methods for the
new solvency test for Swiss insurance undertakings, which will be in
force as of 2005. Before joining FOPI he was assistant professor at the
Department of Operations Research and Financial Engineering (ORFE) at
Princeton University. Damir Filipovic received his PhD in mathematics
from ETH Zurich in 2000, where he is still affiliated as senior researcher.
Abstract
Swiss solvency test for insurers
I present and discuss the principles of the Swiss solvency test for
insurers with regard to Solvency II.
Dr Marcus Fleck, Dresdner Bank
Slides
Marcus Fleck joint Group Risk Control of Dresdner Bank AG in 2001 in the beginning
focussing mainly on market risk issues. As a member of the Strategic Risk & Treasury
Control Department he started in 2002 to contribute to the ongoing Basel II consultation
process in particular on questions regarding counterparty risk modeling for derivatives
portfolios. Marcus Fleck obtained a PhD in theoretical physics from the Max-Planck
Institute for Solid State Research and the University of Stuttgart.
Abstract
New Methods for measuring counterparty exposure consistent with Basel II Capital Accord
The Basel Committee acknowledged only recently that trading book issues
have not been given sufficient attention over the past five years, and
that the Committee had taken too conservative approach to counterparty
risk of derivatives and repo-styled transactions.
The stochastic nature of the default process combined with volatility in
derivatives prices is a challenge not only for supervisiors but also for
banking industry. Based on results from Monte Carlo Simulations we present
new methods for measuring counterparty risk consistent
with the Basel II framework. A fruitfull dialogue between industry
representatives and the Basel Committee on those results has started
already.
Dr Jürgen Hakala, Commerzbank
Slides
Jürgen Hakala is Head of Quantitative Research in Commerzbank ZGS FX.
His research areas are models and products for foreign exchange derivatives and
hybrid interest rate and foreign exchange models. Computational Finance is
a key element for all his activities.
He received a masters degree in theoretical physics from the University of Karlsruhe
and a Ph.D. in mathematics from the University of Bonn at the institute for Neural Networks.
Abstract
Higher order methods and non-uniform grid discretization in finite difference
schemes for exotic option pricing
Higher order methods and non-uniform grid discretization in finite difference
schemes for exotic option pricing.
Prof Dieter Hess, HfB, Frankfurt
Slides
Dieter Hess is currently Professor of Finance at the the Hochschule für
Bankwirtschaft (Business School for Banking and Finance) in Frankfurt
and Lecturer at the University of Karlsruhe. He worked several years at
the Research Center for International Economic Integration and at the
Center of
Finance and Econometrics at the University of Konstanz and published
articles on the microstructure of financial market, risk estimation,
and announcement effects.
Abstract
Does Information Quality Explain Asymmetric Price Reactions
It is well documented that the unanticipated news in the U.S. employment
report trigger strong price reactions in bond markets around the world.
Bayesian updating suggests that the quality of information, i.e. its
precision, acts as a catalyst in determining the strength of the price
reaction to a given piece of unanticipated information. However, it is
difficult to test for this catalyzing effect due to a lack of precision
data. Employing additional detail information, we extract release-specific
precision measures. Based of these precision proxies, we show that prices
respond significantly stronger to more precise information, even after
controlling for an asymmetric price response to 'good' and 'bad' news.
This is joint work with Nikolaus Hautsch.
Dr Peter Neu, Dresdner Bank
Slides
After obtaining a degree in Physics from the Imperial College, London, and
from the University of Heidelberg (Diploma, PhD), Peter Neu held a Post-Doc
position at the Massachusetts Institute of Technology (MIT) in Cambridge,
MA, where he specialized in stochastic dynamics of physical and chemical
systems. In 1997 Peter joined Group Risk Control of Dresdner Bank AG. As a
member of Group Strategic Risk & Treasury Control he worked at various
market and credit risk projects and was heavily involved in building
Dresdner's economic capital model. Since 2001 he is heading a team being
responsible for liquidity risk control, which works in close co-operation
with the Group Funding and Liquidity Management within Treasury.
Abstract
Statistical Mechanics of Financial Markets and Applications in Risk Management
An overview is given how concepts from statistical physics of
disorder systems like scaling, universality, criticality, and
bubble nucleation can be used to explain so called "stylized"
facts of financial time series. Such facts, which cannot be
explained by the in banking popular log-normal
diffusion model, are, e.g.,: Pareto distributed stock returns,
long-ranged temporal volatility correlations (vs. short-ranged
temporal stock return correlations), or negative
return-volatility correlations. Besides the importance for market
risk management it is shown how the dynamics underlying such
phenomena is important for stress testing and capital allocation
to credit risk and operational risk.
Dr Thorsten Oest, d-fine
Slides
Thorsten Oest is senior consultant at d-fine GmbH where he was
involved in implementation projects for risk, market data and treasury
systems. He holds a MSc in mathematical finance from Oxford university
and a PhD in experimental physics from the university of Hamburg.
Before joining d-fine he was a research fellow at CERN (Geneva) and at
DESY (Hamburg) working on data analysis for large physics experiments.
Abstract
A New Approach To Option Pricing For Discrete Hedging And
Non-Gaussian Processes
The Black-Scholes option pricing method is correct under certain
assumptions, among others continuous hedging and a log-normal underlying
process. If any of these two assumptions is not fulfilled, a risk-less
replication of an option is in general not possible.
To handle this case, a new pricing method is proposed. In contrast to other
methods, not the risk of a hedging portfolio, but the option price is
minimized. For the option price minimization the ratio of the averaged
return to the averaged risk of the hedging portfolio is fixed. This
resulting hedging procedure makes the option most competitive on the
market.
A case study for realistic European plain vanilla and binary options was
done. Compared to other methods, the option price is up to 10 % lower. In
the continuous time limit for a log-normal process, the result of the
method converges towards the Black-Scholes result.
Dr Alex Popovici, Bonn University
Slides
Dr Alex Popovici is a research assistent at the University of Bonn. His
research focus lies on equity models with stochastic volatility and jumps,
equilibrium markets in continuous time, numerical methods for pricing and
hedging exotic and structured products (Monte Carlo, numerical PDEs, Fourier
methods). He received a 'Diploma' (Masters) in Mathematics, a 'Diploma' in
Computer Science and a PhD from Bonn University and holds a DEA (Masters)
degree in 'Probability and Finance' from Paris VI University.
Abstract
Numerical analysis of extended Black-Scholes models
The multidimensional Black-Scholes model has been used as a basic and very
effective tool for the valuation of derivative instruments in financial
markets. In the last years empirical observations from the market (excess
kurtosis, fat tails, smile and skew patterns of volatility surfaces, structural
dependency between assets) hinted to the fact that the classical Black-Scholes
framework is too restrictive for an accurate modelling of multidimensional
financial markets. An extension of the Black-Scholes model focusing on the
interdependency structure of assets and which delivers excellent result for
pricing and hedging multi-asset financial derivatives was introduced by
Albeverio and Steblovskaya in 2002. The aim of the talk is to present a
numerical implementation of this model (historical estimation vs. calibration
of parameters, pricing methods) and practical results obtained using market
data (exotic options on baskets, volatility surfaces, etc). The advantages and
drawbacks of this model will be discussed.
Prof LCG Rogers, University of Cambridge
Slides
Chris Rogers is Professor of Statistical Science at the
University of Cambridge, where he moved in 2002 after nearly nine
years at the University of Bath.
He is the author of more than 100 publications, including the famous
two-volume work, Diffusions, Markov Processes, and Martingales with
David Williams. His Finance papers include the potential approach to
term structure of interest rates, complete models of stochastic
volatility, portfolio turnpike theorems, improved binomial pricing,
and Monte Carlo valuation of American options. Chris is
co-editor of Finance and Stochastics and an associate editor of
several journals, including Mathematical Finance. He is a frequent
speaker at industry conferences and courses.
Abstract
Modelling liquidity and its effects
Liquidity is an important effect in the markets, yet it is
hard to come up with a good definition, which not only has
some economic explanation but also retains a reasonable degree
of tractability. In this paper, we propose a simple microeconomic
model in discrete time which carries over to the continuous-time
setting; this results in a modification of the usual dynamics
of portfolio wealth, which appears to be impossible to analyse
exactly, though some asymptotic analysis can be carried through.
Prof Wolfgang Schmidt, HfB, Frankfurt
Slides
Wolfgang M. Schmidt is currently Professor for Quantitative
Methods at the Hochschule für Bankwirtschaft (Business School for
Banking and Finance) in Frankfurt. From 1992 to 2002 he was
Director and Head of Research and Analytics at Deutsche Bank AG in
Frankfurt. Prior to joining Deutsche Bank he held teaching and
research positions at the University of Jena, Berlin, Moscow and
Tbilissi. He graduated in Mathematics from Dresden University of
Technology and holds a PhD and Habilitation in the field of
probability theory from the University of Jena. Prof. Schmidt is the
author of research papers in the fields of probability
theory, stochastic processes and mathematical finance as well as
co-author (with S. Assing) of the book ''Continuous Strong Markov
Processes in Dimension One - A Stochastic Calculus Approach'',
Springer Verlag . His current research interests include mathematical
finance, risk management, credit default modelling, term structure
modelling.
Abstract
Hedging Basket Credit Derivatives with CDS
We investigate the pricing of basket credit derivatives
and their hedging with single name credit default swaps (CDS). The
market in credit default swaps quotes fair insurance premiums (spreads)
whose dynamics is the natural starting point of our model. Pricing
basket credit derivatives requires a model for the dependencies
between the default times. In case of a pure jump filtration,
dependencies are characterized by default implied spread changes.
In this setup we derive a simple system of integral equations
involving the notional amounts of the dynamic hedge positions,
the price and the spread of a basket derivative. We provide some
numerical examples of explicit hedging strategies and valuations
of first-to-default baskets illustrating the approach.
Prof Robert G Tompkins, HfB, Frankfurt
Slides
Dr. Robert G. Tompkins was born in Oklahoma, USA and he received his A.B. (1980),
his A.M. (1980) and his MBA (honors) (1986) from the University of Chicago. He moved
to England in 1986 and subsequently became a British citizen. He earned a Ph.D. (1998)
from the University of Warwick and his Habilitation (2000) from the University of
Technology, Vienna, where Dr. Tompkins lived from 1998 to 2003.
Abstract
Unconditional Return Disturbances: a Non Parametric Simulation Approach
Simulation methods are extensively used in Asset Pricing and Risk
Management. The most popular of these simulation approaches, the Monte
Carlo, requires model selection and parameter estimation. In addition,
these approaches can be extremely computer intensive. Historical
simulation has been proposed as a non-parametric alternative to Monte
Carlo. This approach is limited to the historical data available.
In this paper, we propose an alternative historical simulation approach.
Given a historical set of data, we define a set of standardized
disturbances and we generate alternative price paths by perturbing the
first two moments of the original path or by reshuffling the disturbances.
This approach is totally non parametric when constant volatility is
assumed, or semi-parametric in presence of GARCH (1,1) volatility and is
shown without a loss in accuracy to be much more powerful in terms of
computer efficiency than the Monte Carlo approach. This approach is
extremely simple to implement and is shown to be an effective tool for the
valuation of financial assets.
We apply this approach to simulate pay off values of options on the S&P 500
stock index for the period 1982-2003. To verify that this technique works,
the common back-testing approach was used. The estimated values are
insignificantly different from the actual S&P 500 options payoff values for
the observed period.
This is joint work with Rita L. D'Ecclesia.
JEL classifications: C15, G13, G19
Keywords: Simulation Methods, Historical Simulation, Stochastic
Volatility, Back-testing.
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