
Derivatives and Risk Management in Theory and Practice
1516 March 2010
Dr. Carole Bernard, University of Waterloo
Carole Bernard is currently assistant professor in mathematical finance and
actuarial science at the university of Waterloo, Canada.
She obtained her PhD from the University of Lyon in France.
Her research interests lie at the intersection of Finance, Insurance and Economics.
For example she wrote recent papers in financial engineering
(i.e. about the pricing of barrier and Parisian options, and about hedging volatility risk),
in behavioral finance (about the demand for retail structured products)
and in insurance (about longterm pathdependent options embedded in
equity indexed annuities).
Abstract
Pathdependent Inefficient Strategies and How to Make Them Efficient
We make the following assumptions. (1) Agents’ preferences depend only on the probability
distribution of terminal wealth. (2) Agents prefer more to less.
(3) The market is perfect and frictionless. (4) The market is arbitragefree and
could be incomplete. Under these assumptions, we show that in general pathdependent
strategies are inefficient and not optimal. In addition, we characterize the ones that
are costefficient. We obtain an explicit formula for the efficiency cost of a
strategy as well as for the payoff of the costefficient derivative that
should be preferred by all investors. Finally, we show that in the Black
and Scholes framework, the necessary and sufficient conditions for a
strategy to be costefficient is that its terminal payoff is an increasing
function of the stock price. We illustrate the sudy by exhibiting the specific
form of a derivative that dominates the lookback option, the geometric
Asian option or the barrier option.
This is joint work with Prof. Phelim Boyle.
Christoph Becker, Frankfurt School of Finance & Management
Christoph Bekcer is completing his PhD at the Frankfurt School of Finance & Management,
under the supervision of Prof. Dr. Wolfgang M. Schmidt.
His main research interests are modelling the dependencies between financial assets,
and exploring their consequences in risk management and asset allocation.
Previously, he completed studies in Applied Mathematics at the University of Trier (German Diplom).
Christoph was an intern with Commerzbank and with KPMG,
and has consulted for MathFinance AG and Tachyles Ltd.
Abstract
StateDependent Dependencies: A ContinuousTime Dynamics for Correlations
We propose a new asset price model in continuous time where correlations and
volatilities are functions of the current state of the market. The state of the market
is based on a window of past asset realisations, the length of this window being
a measure for the memory of the market. The approach is motivated by empirical
findings from regression analyses in discrete time. A maximum likelihood
approach is developed to estimate the parameters of the model from discrete asset
realisations. We find strong empirical evidence that correlations increase in bear
markets and for the existence of financial contagion in international markets. We
analyse the severity of financial contagion dependent on market conditions. We
explore consequences of marketstate dependent volatilities and correlation in financial
risk management and option pricing theory. We investigate the variance
as a measure of portfolio risk and compare the variance from a model with constant
correlation with the variance of a model with state dependent correlation.
We propose a measure for losses in diversification due to a potential correlation
breakdown.
This is joint work with Prof. Wolfgang Schmidt.
Dr. Andreas Binder, MathConsult
Andreas Binder received his Ph.D. in Applied Mathematics (University of Linz) in 1991.
After some academic years (Oxford, Linz), he joined MathConsult in 1996 as CEO.
He is also managing director of the Industrial Mathematics Competence Center (IMCC)
and member of the advisory board of the Austrian Mathematical Society.
His book “Einführung in die Finanzmathematik” (coauthored with Hansjörg Albrecher
and Philipp Mayer) appeared in Birkhäuser Verlag in 2009.
Abstract
Using Different Error Functionals in the Calibration of Stochastic Volatility Models
Stochastic volatility models and models including jump processes like the Heston
and the Bates model gain more and more interest in the community.
For practical purposes, it is essential that a fast and stable
calibration routine is available. This calibration is quite frequently
intrinsically instable due to the inverse problem nature of the taks.
In this talk, we study the use of different error functionals (L1,L2 norm)
and minimization algorithms (local and global) for solving the inverse problem.
We also report the influence of the different parameter sets obtained on the price of
exotic options. In order to speed up the calculations especially when using global optimization
techniques we ported the code to run on GPUs.
This is a joint work with M. Aichinger and J. Fürst.
Alexander Giese, Unicredit Markets and Investment Banking
Alexander Giese is CoHead of Financial Engineering
Equities, Commodities and Funds at Unicredit Markets and
Investment Banking which he joined in 2002. He studied financial
mathematics at the Technical University of Berlin and also holds
an MSc from Florida State University in Financial Mathematics.
Abstract
Structured Equity Derivatives with Issuer Risk
During the recent financial crisis the credit spreads of banks skyrocketed from
a few basis points at the beginning of 2007 to several hundreds of basis points
end of 2008. As a result, the issuer risk has become a very important pricing
factor in the valuation of equity linked structured notes issued by banks.
One standard approach of incorporating issuer risk into the pricing of equity
products assumes independence between the equity underlyings and the credit
risk of the issuer and simply multiplies the equity dependent cash flows
with the survival probability of the issuer. Since equity underlyings
and credit spreads are highly negatively correlated, significant mispricing
can be the result of applying such an approach. During the talk,
we introduce several hybrid equity credit models which allow for equity
credit correlation. Using these hybrid models we analyse the impact of
the equity credit correlation on the fair values of representative equity
linked structures with issuer risk.
Dr. Jürgen Hakala, EFG Financial Products
Jürgen is with EFG Financial Products, the derivatives house of EFG,
involved in modelling and financial engineering for all asset classes.
His initial interest was foreign exchange, where he is coeditor of a
textbook about FX derivatives. He is a regular speaker at a variety of conferences.
Abstract
AutoDifferentiation in Finance: A Casestudy
AutoDifferentation is a programming technique that uses functioncomposition and the mechanical
application of the chain rule to obtain derivative expressions by the evaluation of a multivariate function.
We show that this technique is a useful tool for selected applications in finance:
model calibration – replacing the finite difference Jacobian by AD.
Monte Carlo Simulation – augmenting the pathwise, and/or likelihood ratio method.
Dr. Christian Kahl, Commerzbank
Christian Kahl is a Financial Engineer in the Equity and Commodity group of Commerzbank, which he
joined in 2009 from ABN Amro, where he was working on exotic Equity, Hybrid and
Commodity derivatives. His reasearch focus include stochastic volatility models and computational
finance, in particular numerical solutions of Fourier inversion applications. He holds a doctor
degree in numerical analysis from the University of Wuppertal.
Abstract
Modelling CreditHybrid Products
We present an extended multifactor stochastic hazard rate model, where pricing of contingent claims
is done via a partial(integro) differential equation, by introducing a default copula.
This lattice copula is then compared to correlating the default event times, which is the common
approach within a Monte Carlo approach. Analytical results for the short time step limit of the
partial(integro) differential equation implementation are derived and linked to the lower
tail dependency of the respective copula.
Sebastien Kayrouz, Murex
Sebastien Kayrouz is Manager of Foreign Exchange Derivatives at Murex.
Sebastien Kayrouz joined Murex in Paris eight years ago.
Seba is a telecommunications engineering graduate of
Beirut Saint Joseph University School of Engineering.
Prior to working on the crossasset volatility framework,
Seba focused on the validation and market testing of
Murex' Tremor stochastic/local volatility hybrid model.
Sebastien is based in Murex NA, New York.
Abstract
Logical SpaceTM
Time interpolation in the varied forms of strike or moneyness space are not logical,
interpolation in delta space raises questions and encounters computational problems.
We aim to present a new “Logical SpaceTM” for volatility modelling, applicable to all
asset classes and adding transparency to skewness and leptokurtosis.
This is a joint presentation with Dr.Gerd Zeibig.
Prof. Steve Kou, Columbia University
Steve Kou is Professor in the Department of Industrial Engineering and Operations Research at
Columbia, where he teaches Financial Engineering. He is a specialist in mathematical
finance and is wellknown internationally for his research on exotic options,
jump diffusion models, and credit risk. Some of his results have been widely used in Wall Street,
and have been incorporated into standard MBA textbooks, such as the textbook by John Hull.
Abstract
Clustering Defaults and Pricing of Collateralized Debt Obligations
The past several years have been an eventful period for the U.S.
financial markets, mainly due to the crisis in subprime credit markets
and the difficulty in modeling collateralized debt obligations (CDOs).
In this paper we shall propose a model for CDOs that can incorporate
clustering defaults. The model is based on Polya processes and the
cumulative intensity of counting processes. Empirical evidences
suggest that the model can calibration the current CDO data very well.
Prof. Dilip Madan, University of Maryland
Dilip Madan is Professor of Finance at the Robert H. Smith School of Business.
He specializes in Mathematical Finance. He also serves as a consultant to Morgan Stanley,
Caspian Capital LLC, and the FDIC. He is a founding member and immediate Past President
of the Bachelier Finance Society, CoEditor of Mathematical Finance and Associate Editor
for the Journal of Credit Risk and Quantitative Finance. His work is dedicated to
improving the quality of financial valuation models, enhancing the performance of
investment strategies, and advancing the understanding and operation of efficient
risk allocation in modern economies. Recent major contributions have appeared
in Mathematical Finance, Finance and Stochastics, Quantitative Finance,
Journal of Computational Finance, among other Journals.
Abstract
Capital Requirements,Acceptable Risks and the Value of the Taxpayer Put
Limited liability for the firm in the presence of unbounded liabilities delivers
a free put option to the firm that is rarely valued and accounted for. We christen
this put option the taxpayer put. In addition the optimality of free markets is
called into question by the introduction of adverse risk incentives exaggerated by
compensation aligned to stock market values. In such a context we introduce the
concept of socially acceptable risks, operationalized by a positive expectation
after distortion of the distribution function for risky cash flows. This results
in a definition of capital requirements making the risks undertaken acceptable
to the wider community. Enforcing such capital requirements can mitigate the
perverse risk incentives introduced by limited liability provided that the set of
acceptable risks is suitably conservatively de.ned. Additionally the value of the
free taxpayer put may be substantially reduced. We illustrate all computations
for the six major US banks at the end of 2008.
Dr Fabio Mercurio, Bloomberg
Fabio is a Senior Business Manager at Bloomberg LP, New York joining them in 2008 as a senior quant researcher.
Previously, he was the head of Financial Engineering at Banca IMI, Milan providing quantitative support to the
bank's desks of equity, interestrate, forex and creditderivatives trading.
Fabio is the most cited author in Risk Magazine for the year 2008. He has published extensively
in books and international journals. He has jointly authored the book
‘Interest rate models: theory and practice’, (Springer ’01/’06) and edited the book
‘Modelling Interest Rates: Advances in Derivatives Pricing’ (Risk Books ‘09).
He has been an Adjunct professor at Bocconi University and a course teacher both for Risk and Marcus Evans.
Fabio holds a BSc in Applied Mathematics from the University of Padua and a PhD
in Mathematical Finance from the Erasmus University of Rotterdam.
Abstract
Libor Market Models with Stochastic Basis
We start by describing the major changes that occurred in the quotes of market rates after
the 2007 subprime mortgage crisis. We then show how to price interest rate swaps under
the new market practice of using different curves for generating future LIBOR rates and
for discounting cash flows. Straightforward modifications of the market formulas for caps
and swaptions will also be derived.
Finally, we will introduce a new LIBOR market model, which will be based on modeling the
joint evolution of FRA rates and forward rates belonging to the discount curve.
We will start by analyzing the basic lognormal case and then add stochastic volatility.
Dr. Attilio Meucci, Bloomberg
Attilio Meucci leads the research effort of ALPHA, the portfolio analytics and risk platform at Bloomberg.
Concurrently he is adjunct professor at the Master's in Financial Engineering  Baruch College  CUNY.
Previously, Attilio was a researcher at Lehman Brothers, a trader at the hedge fund Relative Value
International, and a consultant at Bain & Co.
Attilio is the author of Risk and Asset Allocation  Springer and several other publications in practitioners
and academic journals. He teaches graduate courses on quantitative risk and portfoliomanagement
worldwide and he is frequently invited as a speaker to conferences, financial institutions and universities.
Attilio Meucci holds a BA summa cum laude in Physics from the University of Milan, a MA in Economics
from Bocconi University, a PhD in Mathematics from the University of Milan and he is CFA chartholder.
Attilio is fluent in six languages and loves physical activity in the outdoors.
Abstract
Managing diversification
We propose a unified, fully general methodology to define, analyze and act on diversification in any environment,
including longshort trades in highly correlated markets. First, we build the diversification distribution,
i.e. the distribution of the uncorrelated bets in the portfolio that are consistent with the portfolio constraints.
Next, we summarize the wealth of information provided by the diversification distribution into one
single diversification index, the effective number of bets, based on the entropy of the diversification distribution.
Then, we introduce the meandiversification efficient frontier, a diversification approach to portfolio optimization.
Finally, we describe how to perform meandiversification optimization in practice in the presence of
transaction and market impact costs, by only trading a few optimally chosen securities.
Dr. Rolf Poulsen, University of Copenhagen
Rolf Poulsen has a PhD from the University of Aarhus, Denmark, and is
currently professor of Mathematical Finance at the University of Copenhagen.
His research interests include derivative pricing (with a view towards model risk)
and mortgage choice.
Abstract
Empirical Performance of Models for Barrier Option Valuation
In this paper the empirical performance of alternative models for barrier option
valuation is studied. Five commonly used models are compared:
the BlackScholes model, the constant elasticity of variance model,
the Heston stochastic volatility model, the Merton jumpdiffusion model,
and the infinite activity Variance Gamma model. We employ timeseries data
from the USD/EUR exchange rate market, and use plain vanilla option prices
as well as a unique dataset of observed market values of barrier options.
The different models are calibrated to plain vanilla option prices, and
crosssectional and prediction errors for plain vanilla and barrier option
values are investigated. For plain vanilla options, the Heston and Merton models
have similar and superior performance both in crosssection and for prediction horizons
of up one week. For barrier options, the performances of continuouspath models
(BlackScholes, constant elasticity of variance, and Heston) is a mixed picture,
while both models with jumps (Merton and Variance Gamma) perform markedly worse.
Dimitri Reiswich, Frankfurt School of Finance & Management
Dimitri Reiswich is a PhD student at Frankfurt School of Finance and Management.
He has a Diploma in Business Mathematics from the University of Hamburg.
Dimitri’s research interests include volatility smile analyses and their
relation with riskneutral densities with a focus on FX smiles.
Abstract
Potential PCA Interpretation Problems for Volatility Smile Dynamics
The typical factor loadings found in PCA analysis for financial markets are commonly
interpreted as a level, skew, twist and curvature effect. Lord and Pelsser question
whether these effects are an artefact resulting from a special structure of the
covariance or correlation matrix. They show that there are some special matrix classes,
which automatically lead to a prescribed change of sign pattern of the eigenvectors.
In particular, PCA analysis on a covariance or correlation matrix which belongs to
the class of oscillatory matrices will always show n1 changes of sign in the nth eigenvector.
This is also the case in most PCA results and raises the question whether the observed
effects have a valid economic interpretation. We extend this line of research by
considering an alternative matrix structure which is consistent with foreign exchange
option markets. For this matrix structure, PCA effects which are interpreted as shift,
skew and curvature can be generated from unstructured random processes.
Furthermore, we find that even if a structured system exists, PCA may not be
able to distinguish between these three effects. The contribution of the factors
explaining the variance in the original system is incorrect.
Prof. Ekkehard Sachs, University of Trier
Ekkehard Sachs is a Professor at the University of Trier and previously has held
positions at Virginia Tech and North Carolina State University. He is an expert
in numerical methods for optimization problems, in particular with partial differential
equations and serves on various editorial boards of international journals in
optimization. He has published three books and more than 100 research papers. His
interest in finance is in calibration and hedging of options and, in particular,
the numerical aspects of these tasks.
Abstract
Adjoint Techniques in Calibration
The pricing of derivatives in the financial markets becomes an increasingly important
area of application for numerical analysis and numerical optimization. Various
mathematical models are currently under consideration, which can be described by
stochastic differential equations, partial differential equations or even explicit
solution formulas. All these models contain a number of parameters that need to be
fit such that the model output resembles the market data as closely as possible.
This constitutes a nonlinear least squares problem and requires efficient and fast
solvers from numerical optimization.
Any fast optimization solver relies on accurate gradient information which, if obtained
from finite difference approximation, works well as long as the number of parameters is
small. However, for a larger number of parameters like time dependent parameters, the
computing time requirement for the gradient calculation can be enormous. In this talk
we illustrate how to replace the finite difference or sensitivity approach by an adjoint
approach which yields a substantial savings in computing time and is applicable in a SDE
or PDE framework. Furthermore, we discuss the use of reduced order models. Here e.g. the
PDE is replaced by a system of ordinary differential equations which is then used in
calibrating the model. Finally, the overall optimization effort in calibrating a PDE
model can be reduced to an effort equivalent to a few evaluations of a PDE.
Dr. Christof Schmidhuber, Fintegral Asset Management
Christof Schmidhuber is founder and managing partner at Fintegral Asset Management.
Before, he was Global Head of Risk Management for Credit Suisse hedge fund investments.
He and his teams in New York and Zürich were responsible for operational due diligence
and market risk monitoring of several hundred managers. He exercised the veto for funds
and portfolios in the investment committees. Prior to joining Credit Suisse in 2004,
Christof Schmidhuber was deputy head of the quantitative group at RMF Investment Products,
where his responsibilities included hedge fund portfolio construction, strategic
asset allocation, due diligence on quantitative managers and the management of research projects.
Dr. Schmidhuber received his Ph.D. in Theoretical Physics in 1993 from the California
Institute of Technology with a thesis on superstring theory.
Subsequently he worked as a Postdoc at Princeton University, as Heisenberg fellow at CERN,
and as Privatdozent for Physics at the University of Berne.
Abstract
Alternative Beta in Practice
The asset allocation process of an investor typically involves an optimization process:
its objective is to maximize expected return subject to constraints such as risk tolerance
or A&L; matching. Traditional market factors, including equity indices or interest rates,
are usually dominant, but sometimes more or less sophisticated trading strategies also
play a role to enhance returns. Recently, socalled “alternative market factors” have
attracted much attention. They represent systematic trading strategies, such as momentum
or contrarian strategies. Exposure to these new market factors has been called “alternative beta”.
It has been advocated that alternative beta can be used to replicate the performance of some of
these sophisticated strategies with much improved liquidity and transparency. In this talk we
propose a classification scheme for the most important forms of alternative beta. We show how
the corresponding alternative market factors can be combined with traditional market factors in
order significantly improve the riskreturn profiles of investment portfolios. We also investigate
the effectiveness of alternative market factors in replicating noninvestible hedge fund indices,
based on one year of real trading
Prof. Uwe Schmock, Technical University of Vienna
Slides
Dr. Uwe Schmock is professor and head of the Institute for Mathematical Methods
in Economics at the Vienna University of Technology.
He is working in the research group for financial and actuarial mathematics and leads the
Christian Doppler Laboratory for Portfolio Risk Management (PRisMa Lab),
a largescale research cooperation with financial industry partners (Bank Austria,
ÖBFA, FJA) in Vienna. He also serves as vice president of the Actuarial Association
of Austria. His main research interests are currently in modelling and estimation of
stochastic dependence with applications in risk management.
Dr. Schmock was formerly research director of RiskLab at ETH Zurich and director of the
Master of Advanced Studies in Finance, offered by ETH and University of Zurich.
Abstract
Generalization of the DybvigIngersollRoss Theorem and Asymptotic Minimality
The longterm limit of zerocoupon rates with respect to the maturity does not always exist.
In this case we use the limit superior and prove corresponding versions of the DybvigIngersollRoss theorem,
which says that longterm spot and forward rates can never fall in an arbitragefree model.
Extensions of popular interest rate models needing this generalization are presented.
In addition, we discuss several definitions of arbitrage, prove asymptotic minimality
of the limit superior of the spot rates, and illustrate our results by several
continuoustime shortrate models.
This is joint work with Verena Goldammer.
Dr. Roland Seydel, dfine
Roland Seydel is a senior consultant with dfine GmbH, where he is member of the Applied Financial
Engineering business unit. His interests range from numerical methods for option pricing
and stochastic and impulse control in finance to nonlinear PIDEs. Roland holds an MSc in Financial
and Industrial Mathematics from the Technical University of Munich. From 2007 to 2009,
he conducted his PhD thesis under the supervision of Prof. Rüdiger Frey in Leipzig.
Abstract
The risk of default, credit securitization of a bank and impulse control
Financial instruments such as AssetBacked Securities (ABS) were at the heart
of the unfolding financial crisis of 2007 and 2008.
These securities bundle loans that banks want to dispose of, e.g., subprime home loans.
Before the crisis, ABS were thought to increase diversification of banks and thus to make the financial
system more resilient; although this turned out to be wrong in general, such instruments still are an
important tool for managing the risk of an individual bank.
In our talk, we present a model of a bank in a Markovswitching economy that can reduce
its loan exposure by discrete impulses. We start with an introduction to the model and
its realworld background. The value function of impulse control is associated with the (viscosity)
solution of a PDE called quasivariational inequality (QVI). This QVI is solved numerically,
and practical insights and conclusions from the numerical results are discussed.
This talk is based on joint work with Rüdiger Frey.
Prof. Michel Vellekoop, University of Amsterdam
Michel Vellekoop is currently professor of Actuarial Sciences at the University of Amsterdam.
He obtained his PhD at Imperial College in London, where he worked on nonlinear filtering algorithms
for stochastic processes. His current reseach interests include models for derivative pricing,
with an emphasis on options with early exercise possibilities, and the application of such
models to life insurance problems.
Abstract
Early Exercise Premia for Assets with Dividends
Standard option pricing models usually pay no or little attention to the inclusion of
realistic dividend structures in the model for the underlying asset prices.
In this talk we show how cash dividends can be included in option pricing schemes
in a consistent way, and we study the poperties of American options when dividends are included.
We derive a generalized version of a wellknown integral equation for the early exercise boundary
which allows the inclusion of dividends, and use this to illustrate the differences with the
case where no dividends are present.
Prof. Uwe Wystup, MathFinance
Slides
Uwe Wystup is Professor of
Quantitative Finance, the academic director for the Masters Program in
Quantitative Finance and head of the Department of Finance
at Frankfurt School of Finance and Management.
Before that he worked for Deutsche Bank, Citibank, UBS and Sal. Oppenheim jr. & Cie
and as financial engineer and structurer
in the FX Options trading team of Commerzbank.
He is founder and managing director of MathFinance AG and editor of the MathFinance
Newsletter and the Annals of Finance.
Uwe holds a PhD in Mathematical Finance from Carnegie Mellon
University. He specializes in the quantitative aspects of foreign exchange markets,
international treasury management and structured products.
He published in many scientific journals and wrote two books on Foreign Exchange Risk
and FX Options and Structured Products.
Abstract
Vedic Mathematics: Teaching an Old Dog New Tricks
We show what we all should have learned in high school but didn't: How the authors of the Indian vedas
did mental arithmetics: multiplication  vertically and crosswise,
division  by one more than the one before,
square roots  the duplex method.
Dr. Gerd Zeibig, Murex
Gerd Zeibig is an Applied Quantitative Consultant at Murex.
Having joined the equity team six years ago Gerd is now working crossasset and is overseeing
Murex’ volatility derivatives management. Gerd holds a Ph.D. in pure mathematics from
Kent State University and has published in leading mathematical journals. Gerd is based
in Murex NA, New York.
Abstract
Logical SpaceTM
Time interpolation in the varied forms of strike or moneyness space are not logical,
interpolation in delta space raises questions and encounters computational problems.
We aim to present a new “Logical SpaceTM” for volatility modelling, applicable to all
asset classes and adding transparency to skewness and leptokurtosis.
This is a joint presentation with Sebastien Kayrouz.
