Programme: DAY 1: 5 April
09.30 Copulas: An Introduction
Kjersti Aas, Assistant Research Director, Norwegian Computing Center
Understanding and quantifying dependence is at the core of all modelling efforts in financial econometrics. The linear correlation coefficient, which is the far most used measure to test dependence, is only a measure of linear depend-ence. This means that it is a meaningful measure of dependence if asset returns are well represented by an el-liptical distribution. Outside the world of elliptical distributions, however, using the linear correlation coefficient as a measure of dependence may lead to misleading conclusions. Hence, alternative methods for capturing co-dependency should be considered. One class of alternatives are copula-based dependence measures. In this talk we give an introduction to copulas. We first give the formal definition of a copula, and give some examples of com-monly used copulas. Further we treat the problem of estimating the parameters of a copula, and finally we present algorithms for simulating from these copulas.
11.00 Coffee Break
11.30 Guest Presentation I: A CAPM Copula and its energetic and contagious relatives
William T. Shaw, Chair, Mathematics and Computation of Risk, Departments of Mathematics and Com-puter Science, University College London
Models of dependency in finance range include a variety of postulated multivariate distributions and copula-quantile fusions for getting to grips with a combination of dependency and marginal structures. In this paper we explore the basics of trying to define dependency in a more financially-motivated way by exploiting the natural couplings be-tween assets based on financial principles. Couplings in finance have often been modelled by CAPM models and APT generalizations, and more recently structures based on graph theory and contagion have been proposed. In this note some basic ideas about defining the statistical objects associated with such couplings are suggested, and the simple notion of a CAPM copula is explored in some detail.
13.00 Lunch
14.00 Guest Presentation II—Dependence Modelling in Credit Risk
Thorsten Schmidt, Chemnitz University of Technology
The credit crisis showed that the straightforward application of copulas to areas where the data is scarce is ex-tremely dangerous. We revisit some approaches and propose improvements via factor models. In particular, affine models and models with shot-noise effects can capture typical effects in credit markets.
15.00 Tea
15.30 Pair-Copula Constructions: Even More Flexible Than Copulas
Kjersti Aas, Assistant Research Director, Norwegian Computing Center
In this talk we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set.
17:00 Close
Programme Day 2 : 6 April
09.30 Copulas in Risk Management
Thorsten Schmidt, Chemnitz University of Technology
We describe the use of meta-distributions as a tool for risk-management to couple arbitrary marginal distributions with various dependence concepts.
10.30 Coffee Break
11.00 Extreme Value Theory
Thorsten Schmidt, Chemnitz University of Technology
This presentation covers classical extreme value theory and the peaks-over threshold approaches. Besides the theoretical concepts we discuss application to financial data, estimation and the resulting consequences to risk management.
12.00 Extreme Value Theory II
Peter Ruckdeschel & Nataliya Horbenko, Fraunhofer ITWM
We take up the pace set by Thorsten Schmidt and discuss various alternatives for parameter estimation in Generalized Pareto Distributions as arising from modeling the tail of the severity distribution in the Loss Distribution Approach of actuarial sciences which is frequently used, e.g., in the context of operational risk.
13.00 Lunch
14.00 Portfolio Optimisation with Downside Risk: Mixture distributions with tail events.
Diana Roman, Brunel University
Copulas are used to capture and represent non-linear dependence, particularly in lower-tail dependencies. This presentation describes portfolio models with downside risk control in which extreme event scenarios for asset prices are modelled using copulas.
15.30 Extreme Value Theory Enhanced by Robust Methods
Peter Ruckdeschel & Nataliya Horbenko, Fraunhofer ITWM
The second part of this presentation continues with an introduction to Robust Statistics applied in this context. It explains the robust approach for model deviations, presents key concepts of Robust Statistics such as influence functions and breakdown point and applies these to obtain optimally-robust estimators. Additionally, we include diagnostics to capture local influence, outlyingness, and fitting quality.
17.00 Close
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Dr Peter Ruckdeschel is a research associate at the Financial mathematics group at Fraunhofer ITWM, Kaiserslautern and at the University of Kaiserslautern.
He received his PhD in Statistics at University Bayreuth in 2001 with an award-winning dissertation on Robust Kalman Filtering. He is co-/author of 13 R packages available on the comprehensive R archive network, ranging from integration of automatic markup to R documents, over objected-oriented implementations of distributions to optimally robust estimation. Within the collaborative software development platform r-forge, he is developing—with other authors—R package robKalman. Since his affiliation to ITWM, he has been working on several industry projects covering parameter estimation in stochastic correlation models, quantification of operational risk, and pricing of loans in illiquid markets.
Dr Kjersti Aas, Assistant Research Director, Norwegian Computing Center
Dr. Kjersti Aas is Assistant Research Director at the Statistics Department of the Norwegian Computing
Center (NR) and she is the head of the group working with financial risk management.
She has a large experience in doing applied contract research for banks and insurance companies. Kjersti
is also doing more basic research, and her papers have been published in (among others) The Journal of
Financial Econometrics, Journal of Risk, Insurance: Mathematics and Economics and European Journal of
Finance.
Professor William Shaw holds the Chair in Mathematics and Computation of Risk at the University
College London
Prior to his current position, he was a member of the Financial Mathematics Research
Group, King’s College, London. He received his doctorate in mathematics from the University of Oxford,
and subsequently held post-doctoral positions at the University of Cambridge and MIT, and lecturing
positions at Balliol and Catherine’s Colleges, Oxford. His industry experience includes working as
consultant applied and financial mathematician, as well as specialist in computational finance and equity
derivatives modelling for Quantitative Analysis Group of Nomura International plc.
Professor Thorsten Schmidt
Thorsten Schmidt is Professor in Mathematical Finance at Chemnitz University of Technology since 2008.
Prior to this he was Associate Professor at University of Leipzig and he held a replacement Professorship
from Technical University Munich. He frequently gives courses on interest rate theory, credit risk and
quantitative risk management. Besides his interests in Mathematical Finance, in particular interest rates,
credit risk and energy markets, he has a strong background in statistics and probability theory.
Dr Diana Roman
Dr Roman obtained a PhD from Brunel University, Department of Mathematical Sciences in 2006. The
following year she worked in a KTP (Knowledge Transfer Partnership) project between Brunel Business School and Optirisk Systems, on simulating asset prices for optimisation problems. Since 2007,
she has been a lecturer in the School of Information Systems, Computing and Mathematics, Brunel
University. Her research interests include decision-making in finance, asset allocation, financial optimisation, risk modelling and asset pricing.
Nataliya Horbenko is a Ph.D. student at the Fraunhofer Institute for Industrial Mathematics (ITWM) in
Kaiserslautern, Germany.
Her key interests are modeling and measuring operational risks.
She graduated in Financial Mathematics in Kaiserslautern in 2008 with a thesis on "Rates of Convergence
to Extreme Value Distributions", dealing with different convergence rates of block maxima samples to the
respective asymptotic distributions. In this workshop she presents joint work with Dr. Peter Ruckdeschel
from the Fraunhofer ITWM
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