Frankfurt MathFinance Conference

Derivatives and Risk Management in Theory and Practice

15-16 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 long-term path-dependent options embedded in equity indexed annuities).

Path-dependent 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 arbitrage-free and could be incomplete. Under these assumptions, we show that in general path-dependent strategies are inefficient and not optimal. In addition, we characterize the ones that are cost-efficient. We obtain an explicit formula for the efficiency cost of a strategy as well as for the payoff of the cost-efficient 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 cost-efficient 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.

State-Dependent Dependencies: A Continuous-Time 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 market-state 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” (co-authored with Hansjörg Albrecher and Philipp Mayer) appeared in Birkhäuser Verlag in 2009.

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 Co-Head 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.

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 co-editor of a textbook about FX derivatives. He is a regular speaker at a variety of conferences.

Auto-Differentiation in Finance: A Casestudy Auto-Differentation is a programming technique that uses function-composition 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.

Modelling Credit-Hybrid Products We present an extended multi-factor 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 cross-asset 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.

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 well-known 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.

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, Co-Editor 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.

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, interest-rate, forex and credit-derivatives 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.

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 portfolio-management 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.

Managing diversification We propose a unified, fully general methodology to define, analyze and act on diversification in any environment, including long-short 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 mean-diversification efficient frontier, a diversification approach to portfolio optimization. Finally, we describe how to perform mean-diversification 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.

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 Black-Scholes model, the constant elasticity of variance model, the Heston stochastic volatility model, the Merton jump-diffusion model, and the infinite activity Variance Gamma model. We employ time-series data from the USD/EUR exchange rate market, and use plain vanilla option prices as well as a unique data-set of observed market values of barrier options. The different models are calibrated to plain vanilla option prices, and cross-sectional 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 cross-section and for prediction horizons of up one week. For barrier options, the performances of continuous-path models (Black-Scholes, 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 risk-neutral densities with a focus on FX smiles.

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 n-1 changes of sign in the n-th 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.

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.

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, so-called “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 risk-return profiles of investment portfolios. We also investigate the effectiveness of alternative market factors in replicating non-investible 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 large-scale 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.

Generalization of the Dybvig-Ingersoll-Ross Theorem and Asymptotic Minimality The long-term limit of zero-coupon rates with respect to the maturity does not always exist. In this case we use the limit superior and prove corresponding versions of the Dybvig-Ingersoll-Ross theorem, which says that long-term spot and forward rates can never fall in an arbitrage-free 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 continuous-time short-rate models.

This is joint work with Verena Goldammer.

Dr. Roland Seydel, d-fine Roland Seydel is a senior consultant with d-fine 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.

The risk of default, credit securitization of a bank and impulse control Financial instruments such as Asset-Backed 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 Markov-switching economy that can reduce its loan exposure by discrete impulses. We start with an introduction to the model and its real-world background. The value function of impulse control is associated with the (viscosity) solution of a PDE called quasi-variational 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.

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 well-known 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.

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 cross-asset 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.

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.

Produced by MathFinance AG - Last modified: March 2010