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Derivatives and Risk Management in Theory and Practice
2nd-4th April 2003
Dr Jörg Behrens, Ernst & Young, Switzerland
Jörg is a partner in the Financial Services Risk Management team in Zurich
and also heading the Capital Management & Financial / Business Modeling
team within FSRM.
He received his Ph.D. from ETH Zurich for his research in high-energy
physics at the LEP accelerator of the European Nuclear Research Facility
CERN, Geneva.
Jörg joined Ernst & Young in July 2002 as former head of the Quantitative
Risk Team of Andersen's Financial Risk Management practise which he joined
in December 2000. Prior to that time Jörg held a number of key positions
within the Risk Management area of UBS in London and Zurich. His industry
knowledge includes 9 years of experience in Market and Credit Risk
Management with a special emphasis on Financial and Business Model review
and development. Jörg's deep Financial and Business modeling experience has
gained him expertise in building highly effective and efficient models to
support strategic decision-making at all levels within an organisation.
Jörg's solid business background coupled with his strong technical know-how
have afforded him well to serve as the engagement partner on projects
ranging from those with completely quantitative deliverables to those with
a high-level strategic advisory scope. Jörg serves as the hands-on
engagement partner for projects in the fields of risk quantification,
business process reengineering / optimisation, strategic analysis &
planning (decision-support) and enhancement for credit and market risk with
a special focus on capital management, RAROC (performance measurement) and
all aspects of the new Basel II Accord. He is a regular speaker at various
international conferences.
Abstract
Modelling dependencies: some practical examples
We discuss the impact of modelling dependencies for a few selected
examples of practical relevance.
Dr Stefan Benvegnu, Deutsche Bank
Stefan Benvegnù currently works in the Economic Capital Methodology and Implementation group within
Deutsche Bank´s credit risk management department. His main working areas are credit risk modelling
and securitizations. Prior to this position he worked as consultant in the financial software branch. He
received a diploma in theoretical physics from the University of Karlsruhe
and a Ph.D. in mathematics from the University of Bochum.
Abstract
Credit Risk for CDO Portfolios
A model that assesses the credit risk for a CDO portfolio is
presented. Starting with the introduction of different types of CDOs, it is
shown how a Merton type model can be used to obtain risk characteristics of
different tranches of CDOs. A short comparison to other existing models that
evaluate CDO structures is given.
Dr Nicole Branger, Goethe University
Nicole Branger is a postdoctoral researcher with the derivatives group
lead by Professor Christian Schlag at Goethe University in
Frankfurt am Main. She holds a Ph.D. in economics from the
University of Karlsruhe. Her research areas are derivatives and financial engineering. She
is particularly interested in incomplete markets, interest rate derivatives, and model risk.
Abstract
Is Volatility Risk Priced? Properties of Tests Based on Option Hedging Errors
This paper provides an in-depth analysis of the
properties of popular tests for the existence and the
sign of the market price of volatility risk. These tests
are frequently based on the fact that for some option
pricing models under continuous hedging the sign of the
market price of volatility risk coincides with the sign
of the mean hedging error. Empirically, however, these
tests suffer from both discretization error and model
risk. We show that these two problems may cause the test
to be either no longer able to detect additional priced
risk factors or to be unable to identify the sign of
their market prices of risk correctly. Our analysis is
performed for the model of Black Scholes and the
stochastic volatility (SV) model of Heston. In the model
of BS, the expected error for a discrete hedge is
positive, leading to the wrong conclusion that the stock
is not the only priced risk factor. In the model of
Heston, the expected hedging error for a hedge in
discrete time is positive when the true market price of
volatility risk is zero, leading to the wrong conclusion
that the market price of volatility risk is positive.
If we further introduce model risk by using the BS delta
in a Heston world we find that the mean hedging error
also depends on the slope of the implied volatility
curve and on the equity risk premium. Under parameter
scenarios which are similar to those reported in many
empirical studies the test statistics tend to be biased
upwards. This means that sometimes the test does not
detect negative volatility risk premia, or it signals a
positive risk premium when it is truly zero. The results
of this test furthermore strongly depend on the location
of current volatility relative to its long-term mean,
and the degree of moneyness of the option. As a
consequence the empirical tests may suffer from the
problem that the researcher cannot draw the hedging
errors from the same distribution repeatedly. This
implies that there is no guarantee that the empirically
computed t-statistic has the assumed distribution.
Prof Pierre Collin-Dufresne, Carnegie Mellon University
Pierre Collin-Dufresne is an Associate Professor of Finance at Carnegie
Mellon University. He earned his Ph.D. in 1998 from the HEC School of
Management, Paris, France. Dr. Collin-Dufresne's teaching and research
interests include Asset and Contingent Claim Pricing, Fixed Income
Securities, Default Risk, Emerging Markets, and International Finance. He
has served as a consultant for multiple financial institutions and has
several publications in refereed journals such as the Journal of Finance
and Journal of Derivatives. He is a member of the Center for Computational
Finance of Carnegie Mellon University and an associate editor of the Review
of Financial Studies.
Abstract
Identification and estimation of maximal affine term structure models: an
application to stochastic volatilty
We propose a canonical representation for affine term structure models where
the state vector is comprised of the first few Taylor-series components of the
yield curve and their quadratic (co-)variations. With this representation:
(i) the state variables have simple physical interpretations such as level,
slope and curvature, (ii) their dynamics remain affine and tractable,
(iii) the model is by construction `maximal' (i.e., it is the most general
model that is econometrically identifiable), and (iv) modelinsensitive
estimates of the state vector process implied from the term structure are
readily available. We find that the `unrestricted' A1
(3) model of Dai and Singleton (2000) estimated by `inverting' the yield
curve for the state variables generates volatility estimates that are
negatively correlated with the time series of volatility estimated using
a standard GARCH approach. This occurs because the variance of the short
rate is at the same time a linear combination of yields (i.e., it impacts
the cross-section of yields), and the quadratic variation of the spot
rate process (i.e., it impacts the time-series of yields). We then
investigate the A1 (3) model which exhibits
`unspanned stochastic volatility' (USV). This model predicts that the
cross section of bond prices is independent of the volatility state
variable, and hence breaks the tension between the time-series and
cross-sectional features of the term structure inherent in the
unrestricted model. We find that explicitly imposing the USV constraint
on affine models significantly improves the volatility estimates, while
maintaining a good fit cross-sectionally.
Dr Bernd Engelmann, Bundesbank
Bernd Engelmann is an economist in the Banking Supervision Research Group
of the Deutsche Bundesbank in Frankfurt. He holds a diploma in mathematics
from the University of Augsburg and a PhD in financial economics from the
University of Vienna. He currently works on credit scoring and credit risk
modelling.
Abstract
The Basel II IRB Approach - How Could a Validation Procedure Look Like?
Under the proposed new capital adequacy framework, Basel II, capital
charges for credit risk in the IRB approach are based on several risk
parameters of an individual exposure estimated by financial institutions,
the probability of default, the loss given default, and the exposure at
default. In this talk we will focus on rating systems and analyse several
quality measures we have found in the literature. We will discuss their
usefulness for validation purposes and draw conclusions on how a validation
procedure could look like.
Dr Robert Fiedler, Algorithmics Frankfurt
Robert Fiedler, born 1955 near Frankfurt, studied Mathematics, Computer
Sciences and Philosophy at the Universities of Heidelberg and Darmstadt
where he obtained a PhD in mathematics (differential geometry) and worked
as a scientist and lecturer.
He joined Banque Nationale de Paris in Frankfurt as a money market /
interest rate derivatives trader, later heading up the asset/ liability
management team.
He was Deputy Head of Financial Markets at NatWest Markets in Frankfurt
until he moved to risk management in London.
1997 he joined Deutsche Bank in Frankfurt, where he headed the team in
Group Risk Management dealing with treasury and liquidity risk issues,
reporting to the Group Head of Market- and Operational Risk.
After developing a new methodological framework for funding liquidity risk,
he implemented this approach as a firm-wide liquidity risk IT solution
called LiMA - Liquidity Measurement & Analysis.
Since September 2000 he built as a Senior Director the benchmark solution
for Fundingg Liquidity Risk at Algorithmics Inc., Toronto. Now he heads as
an Executive Director Algorithmics' ALM and Liquidity Risk Solutions.
Abstract
Quantification of Funding Liquidity Risk in a Common Framework with ALM
The quantification of Funding Liquidity Risk is developed and discussed.
The concepts of Expected Liquidity (Forward Cash Exposure), Expected
Liquidity-at-Risk, Counterbalancing Capacity and Day-Count-to-Default are
introduced and it is discussed how they fit into an overall ALM strategy as
well as into more general regulatory / supervisory requirements.
The transfer of methodologies from trading risk to ALM is examined;
difficulties and alterations are discussed and it is considered how they
fit into recent regulatory initiatives (BIS2).
Prof Rüdiger Frey, University of Leipzig
Rüdiger Frey is Professor of Financial Mathematics at the University of Leipzig,
Germany. Prior to that he held positions as Assistant Professor of Finance at the
University of Zurich and as UBS research fellow in financial mathematics at the
Federal Institute of Technology (ETH) in Zurich. He holds a diploma in mathematics
from the Univeristy of Bonn where he received his PhD in financial economics in 1996.
His main research fields are quantitative risk management and the pricing and hedging
of derivatives under incompleteness and market frictions. Rüdiger has published
research papers in leading journals and has given seminars at a number of important
international conferences and institutions. He has also been involved in consulting
projects for Swiss insurance companies and banks.
Abstract
On Dynamic Models for Portfolio Credit Risk and Credit Contagion
It is by now well known that the performance of models for portfolio credit risk is
very sensitive to the modelling of dependence between defaults of different obligors.
In this talk we will be concerned with dynamic models for portfolios of dependent
defaults. After a brief survey of existing approaches, we concentrate on models for
credit contagion, i.e. models where the default of one company has a direct impact on
the default intensity of other firms. We introduce a Markovian model and discuss the
various types of interaction. Finally we present limit results for large portfolios in
a homogeneous model with mean-field interaction and analyze the impact of credit
contagion on the portfolio loss distribution.
Dr Jürgen Hakala, Commerzbank
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
A time-discrete model for forward volatility
Jürgen Hakala, Ulrike Polte, Dimitri Topaj
A model for forward volatilities in a timediscrete volatility setting is
applied to first generation exotic options. To get a tractable simplified
model of the real world the assumption of observable market volatilities
is relaxed to the point that market volatilities are evolving continuously
through time, but can be observed at few points in time only. The
natural question arising within that setting is a suitable hedge strategy
and the implied costs arising from the chosen strategy. The strength of
this approach is the intuitive meaning of the leading terms in a
TaylorExpansion of the pricing equation.
Dr Vicky Henderson, University of Oxford
Vicky Henderson is Nomura Research Fellow at the Nomura Centre for
Quantitative Finance, Mathematical Institute at the University of Oxford.
She previously held postdoctoral positions at RiskLab, ETH Zurich and
FORC at the University of Warwick. Since obtaining her PhD on passport
option pricing from the University of Bath in 1999, Vicky has
published in many leading journals on topics including
comparison of option prices in jump diffusion and stochastic volatility
models, options on non-traded assets, real options, Asian option
symmetries and valuation of executive stock options.
Vicky has presented at numerous international academic and practitioner
conferences and previously worked as a Quantitative Analyst for Westpac,
Sydney.
Abstract
A Comparison of q-optimal option prices in a Stochastic Volatility Model
This paper investigates option prices in an incomplete stochastic
volatility model with correlation. In a general setting, we prove an
ordering result that convex option prices are decreasing in the market
price of volatility risk.
We investigate the q-optimal class of pricing measures. Using the ordering
result, we prove comparison theorems between option prices under the
minimal martingale, minimal entropy and variance optimal pricing measures.
If the mean-variance tradeoff is deterministic, this collapses to the well
known result that option prices computed under these three pricing
measures are the same.
Specialising to the Heston model with mean-variance tradeoff increasing in
volatility, enables us to deduce option prices are decreasing in the
parameter q. Numerical solution of the pricing pde corroborates the theory
and shows the magnitude of the differences in option price due to varying
q. Choice of q is shown to influence the shape of the implied volatility
smile for varying maturity options.
Dr David Hobson, University of Bath
Dr David Hobson is Reader in Statistics at the University of Bath. He also
currently holds an Advanced Fellowship from the EPSRC which means that he
can devote the next five years to research. His background is in
probability theory, but now he works mainly on mathematical finance. He
has worked extensively on stochastic volatility, passport options,
and robust, model-independent bounds for the prices of barrier options.
More generally his research interests concern the pricing of derivative
securities in incomplete markets.
Abstract
Real options, non-traded assets and utility indifference prices
We consider a financial model with both traded and non-traded assets, and
show that the utility indifference (bid) price for a contingent claim on a
non-traded asset is bounded above by the expectation under the minimal
martingale measure. This bound also represents the marginal price for the
claim. The bound and the marginal bid price are independent of both the
utility function and initial wealth of the agent.
Prof Claudia Klüppelberg, Technical University Munich
Slides
Professor Dr. Claudia Klüppelberg holds the Chair of Mathematical
Statistics at the Center for Mathematical Sciences of the Munich
University of Technology.
After her Diploma in Mathematics and a Ph.D. at the University of
Mannheim Claudia Klüppelberg spent five years (1990-1995) as a Postdoc
in the Insurance Mathematics group of the Department Mathematik at ETH
Zurich (with Profs. Hans Bühlmann and Paul Embrechts).
During 1995-97 Claudia Klüppelberg was Associated Professor of Applied
Statistics at the Mathematics Department of the University of Mainz. In
Spring 1997 she accepted an offer of the Munich University of
Technology. She took part in creating a very successful Diploma
Programme in Financial and Economic Mathematics, which started in
October 1997. this Programme contains courses in financial and
insurance mathematics.
Claudia Klüppelbergs research interest combine various areas of applied
probability and statistics, and her work is often motivated by real
life problems. At the moment this concerns mainly the areas of insurance
and finance. Both fields concentrate on financial risk management; the
mathematical models and methods, however, differ.
Besides numerous publications in scientific journals, Claudia
Klüppelberg has coauthored the book Embrechts, P., Klüppelberg, C. and
Mikosch T. (1997, 1999, 2001) Modelling Extremal Events for Insurance
and Finance. Springer, Berlin.
Abstract
Optimal Portfolios with Bounded Capital-at-Risk
We investigate some portfolio problems that consist of maximizing expected
terminal wealth under the constraint of an upper bound for the risk, where we measure
risk by the variance, but also by the Capital-at-Risk (CaR).
The solution of the mean-variance problem has the same structure for any price
process which follows an exponential Lévy process.
For the mean-CaR problem we make use of an approximation of the Lévy
process as a sum of a drift term, a Brownian motion and a compound Poisson process.
Certain relations between a Lévy process and its stochastic exponential
are in vestigated.
Prof Christoph Kühn, Frankfurt MathFinance Institute
Christoph Kühn is Juniorprofessor at the Frankfurt MathFinance
Institute. Prior to that he worked as a post-doctoral researcher at
Vienna University of Technology. He holds a diploma in mathematical
economics from the University of Marburg and a PhD in mathematics from
Munich University of Technology.
His main research fields are pricing and hedging of derivatives in
incomplete market models and models with transaction costs.
Abstract
Game Options: Pricing, Hedging, and Optimal Exercise
A game option (also referred to as Israeli option or recall option)
is a generalization of an American option which also enables the seller
to terminate it before maturity, but at the expense of a penalty.
In the first part of the talk we introduce a general approach how to
price derivatives in incomplete markets which can also be applied to
game options.
Then, we describe the optimal exercise and hedging strategy
for the Israeli put option and present a Monte Carlo valuation approach
similar to Rogers (2002) (joint work with Jan Kallsen
and Andreas Kyprianou).
Dr Jürgen Linde, Dresdner Bank
Jürgen Linde works in the Global Models And Analytics Group at
Dresdner Bank with focus on model validation for interest rate
derivatives. Prior to his current position he was senior
consultant at KPMG's "Financial Risk Management Advisory Group".
He studied mathematics in Heidelberg and received his Ph.D. at
Dortmund's Scientific Computing Faculty where he worked on
numerical techniques for partial differential equations.
Abstract
Efficient Numerical Techniques for Pricing Multivariate Options
The solution of multidimensional PDEs can only be achieved by
interplay of several sophisticated numerical techniques. For
high-dimensional problems it is essential to identify a few
principal components that accurately approximate the full system.
These equations can be dealt with by sparse grid techniques, e.g.
the combination technique that extrapolates the solution from
substantially less degrees of freedom and additionally allows
parallelisation by simple data distribution. For the solution of
lower dimensional problems (or thus reduced systems) efficient
numerical techniques - combining the building blocks
discretisation, grid generation and solver - are at hand. These
methods ensure a stable and high order discretisation. Non-smooth
regions as they typically appear in option pricing problems
can be handled by a priori (e.g. refinement by mesh grading)
or more advanced a posteriori (e.g. adapted to finite element
methods) adaptivity strategies. Large discretised systems can be
solved efficiently by multigrid techniques that can handle
unrestricted problems (resulting from European options) as well as
obstacle problems (stemming from American style options). In
several cases high-order schemes directly yield estimates for
sensitivities.
This is a joint presentation of Dr Jürgen Linde and
Christoph Reisinger.
Dr Fehmi Özkan, University of Freiburg
Fehmi Özkan teaches stochastics and mathematical finance at the
University of Freiburg. He is also a research fellow at the Freiburg
Centre for Data Analysis and Modelling. He got his Ph.D. in
mathematics from the University of Freiburg under the supervision of
Ernst Eberlein in 2002. His research interests are statistical analysis of
financial data and applications of Levy processes in finance, credit
risk and Libor models.
Abstract
Levy processes in credit risk
Mathematical credit risk models in the literature are mainly models
based on Brownian motion although it is known that real-life financial
data provides a different statistical behaviour than that implied by
these models. Lévy processes are an appropriate tool to increase
accuracy of models in finance. They have been used to model stock
prices, and term structures of interest rates, thus allowing more
accurate derivative pricing and risk management. This presentation shows
how Lévy processes can be applied to credit risk models.
Christoph Reisinger, University of Heidelberg
Christoph Reisinger works on option pricing at the Interdisciplinary
Center for Scientific Computing (IWR) at the University of Heidelberg.
Coming from computational fluid dynamics, the field of research covers
numerical techniques for partial differential equations.
Primary interests are currently feasible and accurate discretisations
for high-dimensional PDEs resulting from multivariate option pricing problems.
The focus is on sparse grid and extrapolation methods, which are
coupled with dimension reduction approaches.
Abstract
Efficient Numerical Techniques for Pricing Multivariate Options
The solution of multidimensional PDEs can only be achieved by
interplay of several sophisticated numerical techniques. For
high-dimensional problems it is essential to identify a few
principal components that accurately approximate the full system.
These equations can be dealt with by sparse grid techniques, e.g.
the combination technique that extrapolates the solution from
substantially less degrees of freedom and additionally allows
parallelisation by simple data distribution. For the solution of
lower dimensional problems (or thus reduced systems) efficient
numerical techniques - combining the building blocks
discretisation, grid generation and solver - are at hand. These
methods ensure a stable and high order discretisation. Non-smooth
regions as they typically appear in option pricing problems
can be handled by a priori (e.g. refinement by mesh grading)
or more advanced a posteriori (e.g. adapted to finite element
methods) adaptivity strategies. Large discretised systems can be
solved efficiently by multigrid techniques that can handle
unrestricted problems (resulting from European options) as well as
obstacle problems (stemming from American style options). In
several cases high-order schemes directly yield estimates for
sensitivities.
This is a joint presentation of Dr Jürgen Linde and
Christoph Reisinger.
Dr Richard Rossmanith, d-fine
Richard Rossmanith is Senior Consultant at d-fine GmbH, the former
Financial and Commodity Risk Consulting practice of Arthur Andersen.
He joined Arthur Andersen in 1998, and has subsequently consulted
German banks on quantitative finance, mathematical methods, IT
integration, outsourcing, and regulatory compliance, and in
particular on the issue of financial market data. The latter topic
inspired his MSc thesis for the Mathematical Finance postgraduate
program at Oxford University, and the talk at the conference gives a
brief summary (the thesis is available upon request, or can be
downloaded from www.d-fine.de).
Mr Rossmanith studied Mathematics (and worked as University
Assistant) at Universität Augsburg, Iowa State University in
Ames (USA), and Friedrich-Schiller-Universität Jena, where he
received his Dr. rer. nat. (PhD) for a dissertation thesis on Lie
Algebras, Group Algebras, and Computer Algebra.
Dr Rossmanith has been appointed Honorary Lecturer for Financial
Mathematics by the University of St Andrews (Scotland) since 2000.
Abstract
Data Quality Measures and Completion of Market Data
Data Quality Measures and Completion of Market Data
"Outliers" and "incomplete data" are very common problems that
financial institutions face when they collect financial time series
in IT data bases from commercial data vendors for regulatory,
accounting, and benchmarking purposes. We argue that outlier
detection and data completion are closely (almost interchangeably)
related. Then we present several data completion techniques, some of
which are productively used in practice, and others which are less
established. Finally, optimal completion methods are recommended,
based on an empirical study for the completion of swap and forward
rate curves in the currencies Deutsche Mark (respectively Euro),
Pound Sterling, and US Dollar.
This talk is based on the speaker's thesis for the Mathematical
Finance postgraduate program at Oxford University (the thesis is
available upon request, or can be downloaded from
www.d-fine.de). It represents a snapshot of ongoing market data
and time series research at d-fine, which continues to concern the
speaker and several of his colleagues.
Prof Wolfgang Schmidt, Hochschule für Bankwirtschaft, 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
Modeling Default Dependence with Threshold Models
We investigate the problem of modeling defaults of dependent credits.
In the framework of the class of structural default models we study
threshold models where for each credit the underling ability-to-pay
process is a transformation of a Wiener processes. We propose a model
for dependent defaults based on correlated Wiener processes whose
time scales are suitably transformed in order to calibrate the model to
given marginal default distributions for each underlying credit. At the
same time the model allows for a straightforward analytic calibration
to dependency information in the form of joint default probabilities.
We illustrate the application of the model providing some examples of the
pricing of basket default swaps.
This is a joint paper with Ludger Overbeck.
Prof Ronald Smith, Loughborough University
Slides
Ron Smith is Professor of Applied Mathematics at Loughborough University. His
interest in optimal computation of equations with decay, flow and spread, arose in
the 1990's from work with a team of UK Government scientists on predicting the
isotopic fractionation of nuclear waste in groundwater flows. Computational
improvements allowed a wide spectrum of future climates to be studied for less than
the previous price of a single prediction. The political sensitivity of the isotopes and
possible waste sites precluded open-literature publication of the teams' results. The
computational ideas are not secret and are widely applicable, including to the
Black-Scholes equation in mathematical finance.
Abstract
Optimal compact finite-difference scheme for the Black-Scholes Equation
Compact numerical schemes use the minimum number of successive mesh
points and of time steps. For the Black-Scholes equation this is 3 (arbitrarily-spaced)
share price mesh points by 2 time steps. A general compact numerical scheme would
be a linear implicit equation involving the computed option values at 6 grid points.
Thus, 5 degrees of freedom are available to make the discretization errors be small.
The optimal scheme uses all that adjustability to achieve errors at the grid points of
fifth order in the step length and to all orders in time. There are stability restrictions
upon the permissible time step. Unconditional stability can be achieved at the
sacrifice of one order in the accuracy, or with the simplifications of fixed interest
rate, fixed volatility and specified time-dependence (related to interest rate and
volatility) of logarithmically-spaced grid points. Simple test cases suggest that for
typical levels of accuracy, the computational resources can be 0.001 of conventional
explicit schemes. It would seem feasible to perform the profusion of calculations
needed to span scenarios of changing market rates, asset volatilities and strike prices.
Dr Mikhail Soloveitchik, d-fine
I am a senior-consultant at d-fine (former Financial and Commodity Risk
Consulting practice of Arthur Andersen ).
I studied Mathematics at the Moscow State University (PhD 1989 in probabilty
theory and stochastic processes) and hold a research positionat at the
University of Heidelberg (Habilitation 1997). Last years I work as a consultant
for the financial industry. My interest include quantative mathematical
analysis of financial markets and it's application to practical problems of
financial risk management. I have been working on several projects in German
and Eropean financial institutes.
Abstract
Growth Optimal Portfolios in a semimartingale context
I am a senior-consultant at d-fine (former Financial and Commodity Risk
Consulting practice of Arthur Andersen ).
I studied Mathematics at the Moscow State University (PhD 1989 in probabilty
theory and stochastic processes) and hold a research positionat at the
University of Heidelberg (Habilitation 1997). Last years I work as a consultant
for the financial industry. My interest include quantative mathematical
analysis of financial markets and it's application to practical problems of
financial risk management. I have been working on several projects in German
and Eropean financial institutes.
Dr Robert Tompkins, Hochschule für Bankwirtschaft, Frankfurt
Robert Tompkins is a University Dozent at the Technical University Vienna and has accepted
an Honorary Professorship at the University of Warwick Business School, where he has taught
courses on Financial Markets during the 2000/2001 academic year. He will start at HfB, Frankfurt,
as a Professor of Finance in autumn 2003.
Dr. Tompkins was formerly the Head of International Quantitative Research at Kleinwort Benson
Investment Management. In addition, he remains the Managing Director of the Minerva Group. Prior
to this, he was the Futures and Options Specialist at Merrill Lynch, Europe and an Interest Rate
Options Dealer and Currency Options Trader at two major Chicago banks. He has three degrees from
the University of Chicago, including an MA in Quantitative Methods and an MBA (honours). In
addition, he completed his Ph.D. in Finance at the University of Warwick in 1998 and his Habilitation
in Finanzwirtschaft at the University of Technology, Vienna in 2000.
Robert has authored three books on Options and edited a book on exotic options "From Black Scholes to
Black Holes". Robert is currently writing a series on Exotic Options, which appears in the Austrian
Journal, Bank Archiv. This series will form the basis of a book that will be published by Cambridge
University Press in 2002. He has published widely in RISK Magazine, and a number of academic journals
including Journal of Futures Markets, Journal of Derivatives, Journal of Risk Finance, Journal of Risk,
Quantitative Finance and the European Journal of Finance. Robert's current research interests include
comparisons of established and emerging markets, volatility estimation and forecasting, implied
volatility smile patterns and the hedging of exotic contingent claims.
Abstract
Flexible Complete Models with Stochastic Volatility: Generalising Hobson & Rogers (1998)
Friedrich Hubalek, Josef Teichmann and Robert G. Tompkins
Hobson and Rogers (1998) propose an option pricing model where the
volatility is a deterministic function of the moving average of past
(logarithm of) underlying prices. They show that such a model can also
generate implied volatilities that vary across striking price and term to
expiration. In this research, this model is tested on actual option
markets.
While the Hobson and Rogers (1998) model produces divergences from Black
Scholes (1973) prices on a microscopic scale, we have not been able to
replicate actual option prices with this model. To determine prices from
this model we develop a robust analytic approximation.
To better fit observed options prices, we generalise the model Hobson and
Rogers (1998) by the addition of two additional parameters. This model is
able to match option prices on the British Pound/US Dollar across both the
striking price dimension (smiles) and across different maturities (the term
structure of implied volatility). By use of Mavillian calculus, we are able
to determine partial derivatives of the generalised model and compute
hedging ratios.
Dr Torsten Wegner, d-fine
Torsten Wegner is senior-consultant at d-fine, former Financial and
Commodity Risk Consulting practice of Arthur Andersen. He studied
physics at the Humboldt-University in Berlin where he received his PhD
in 2000. Soon he discovered the challenge of quantitative finance and
studied mathematical finance at the Oxford University.
Since then, he has been been working on several projects in this area.
Abstract
Valuation of Swing Options Considering Seasonality of Power Prices
A log-normal mean-reverting diffusion model with time-dependent
parameters is used to describe the stochastic process followed by
prices at the electricity spot-market. The time-dependence is utilized
to account for effects of seasonality which are an immediate consequence of
the fact that electricity is hard to store.
A Black-Scholes-like derivation is used to give a valuation
model for pricing derivative securities. This model will be applied to swing
contracts. The latter represent a very flexible kind of options
that can even be endowed with contractual penalties.
Different penalty functions are studied within a finite-difference
approximation scheme. The model parameters are calibrated to market data
from the European Electricity Exchange in Leipzig (Germany).
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