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Mini-Conference on Risk Management in Finance and Insurance
organised by

RiskLab (ETHZ) and ISB (Uni. of Zürich)

Location: ETH Zürich, Main Building, Lecture Theatre HG F5. Refreshments in the «Uhrenhalle» (main hall, F-floor)

Time: Friday, October 18, 2002, 8.50 - 16.30

Conference program and abstracts are available online:
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Pictures taken by Susanne Keller (Strategic Excellence Projects, ETH Zürich).
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8.50 - 9.00 Prof. Dr. Paul Embrechts (RiskLab and Dept. of Math., ETH Zürich)
Welcome and Introduction
9.00 - 9.10 Prof. Dr. Rajna Gibson (Swiss Banking Institute, University of Zürich)
The NCCR-Project "Financial Evaluation and Risk Management"
9.10 - 9.20 PD Dr. Uwe Schmock (ISB, Uni. of Zurich and D-MATH, ETHZ)
The New Program "Master of Advanced Studies in Finance"
9.20 - 10.00 Prof. Dr. Karl Frauendorfer (Inst. of Operations Research, Uni. of St. Gallen)
Portfolio Selection Using Multi-Stage Stochastic Quadratic Programming

Abstract: We apply the mean-variance criterion in a multi-period setting to obtain efficient portfolios. The stochastic dynamics of returns are discretized with respect to time and space and are summarized in a scenario tree. Wealth evolves according to the realized returns and the chosen rebalancing strategy while, at the same time, following budget equations. At each instance of decision, the rebalancing activities are connected to transaction and market costs.
     Formally, the portfolio selection model can be seen as a multi-stage stochastic quadratic program with a characteristic dynamic structure induced by the scenario tree of the stochastic dynamics. Multi-stage stochastic quadratic programs are difficult to solve, since their size becomes excessively large even for coarse discretizations. In order to solve these problems adequately, we apply a primal-dual interior point method. To exploit the special problem structure, a highly efficient dynamic programming recursion for the computationally intensive task of solving Karush-Kuhn-Tucker systems is used.
     Numerical results will be presented which illustrate how transaction costs and stochastic correlations affect the diversification. In addition, we will discuss our experiences while working on strategic asset allocation problems.
10.00 - 10.30 Prof. Dr. Philipp J. Schönbucher (Dept. of Math., ETH Zürich)
Copula-Dependent Default Risk in Intensity Models

Abstract: In this talk we present a new approach to incorporate dynamic default dependency in intensity-based default risk models. The model uses an arbitrary default dependency structure which is specified by the copula of the times of default. This is combined with individual intensity-based models for the defaults of the obligors without loss of the calibration of the individual default-intensity models. The dynamics of the survival probabilities and credit spreads of individual obligors are derived and it is shown that in situations with positive dependence, the default of one obligor causes the credit spreads of the other obligors to jump upwards, as it is experienced empirically in situations with credit contagion. For the Clayton copula these jumps are proportional to the pre-default intensity. If information about other obligors is excluded, the model reduces to a standard intensity model for a single obligor, thus greatly facilitating its calibration. To illustrate the results they are also presented for Archimedean copulae in general, and Gumbel and Clayton copulae in particular. Furthermore it is shown how the default correlation can be calibrated to a Gaussian dependency structure of CreditMetrics-type.
10.30 - 11.00 Coffee Break (Main Hall, F-Floor, Uhrenhalle)
11.00 - 11.30 Dr. Gustaf Unger (IFOR, Dept. of Math., ETH Zürich)
Hedging Strategy and Electricity Contract Engineering

Abstract: We discuss how a utility can engineer contracts that can be hedged through production. It is shown how the operational flexibility of a hydro storage plant can be used to hedge adverse movements in the portfolio. We show how in particular the volume risk, which is not hedgeable with standard contracts, can be managed through an intelligent dispatch strategy. Despite the incompleteness in the market, we quantify the value of this operational flexibility.
11.30 - 12.00 Martin Baumann (Dept. of Math., ETH Zürich)
Arbitrage Pricing in Electricity Markets Based on a Model for the Term-Structure of Futures Prices

Abstract: Electricity cannot be stored effectively. This causes a very special price behaviour and clearly distinguishes electricity from other (energy-)commodities. Furthermore, hedging with the commodity is impossible. We will introduce a model for the demand process and the evolution of the supply curve and use them as ingredients for a model of the term-structure of futures prices. These futures will serve as underlyings of a market model, where we will discuss arbitrage pricing.
12.00 - 13.40 Lunch Break
13.40 - 14.10 Prof. Dr. Philippe Artzner (RiskLab and Université Louis Pasteur)
Multiperiod Risk Measurement: Where Are We?

Abstract: It is now time to review and examine various attempts, in the literature as well as in practical applications, at dealing, "statically" or "dynamically", with the question of intertemporal "solvency" or intertemporal "solvency and acceptability". The topic of multiperiod capital assignment for the purpose of performance measurement or even pricing, makes this task much more urgent.
14.10 - 14.40 Dr. Ana-Maria Matache (RiskLab and SAM, Dept. of Math., ETH Zürich)
Fast Deterministic Pricing of Options on Lévy Driven Assets

Abstract: In recent years, awareness of the shortcomings of the Black-Scholes model has increased and more general models for the stochastic dynamics of the risky asset have been proposed, e.g., stochastic volatility models and 'stochastic clocks'. The latter lead to so-called jump-diffusion price processes: the Wiener process from the Black-Scholes model is replaced by a jump-diffusion Lévy process.
     After selection of an equivalent martingale measure Q the asset pricing problem becomes once again the problem of solving a deterministic equation. Contrary to the Black-Scholes case, this equation is now a parabolic integro-differential equation (PIDE) with non-integrable kernel if the jump activity of the Lévy process is infinite.
     We show that the PIDE can be localized to bounded domains and we estimate the error due to this localization. The localized PIDE is discretized by the theta-scheme in time and a wavelet Galerkin method with N degrees of freedom in space. The full Galerkin matrix for A can be replaced with a sparse matrix in the wavelet basis, and the linear systems for each time step are solved approximately in linear complexity. Our deterministic algorithm gives optimal convergence rates (up to logarithmic terms) for the computed solution in the same complexity as finite difference approximations of the standard Black-Scholes equation. Computational examples for various Lévy price processes (Variance Gamma, CGMY) are presented.
14.40 - 15.10 PD Dr. Uwe Schmock (ISB, Uni. of Zurich and Dept. of Math., ETHZ)
How an Insurance Company Loses its Capital Given Ruin Occurs

Abstract: We consider the classical risk reserve process R consisting of the initial capital, the premium income ct minus the claims arriving up to time t. Let v(u) be the first time the risk reserve process falls below -u, where u denotes a credit line. Assuming a positive security loading, we know that the probability of v(u) being finite tends to zero as u tends to infinity. If the distribution of the claims has an exponential moment, then we use results of Asmussen (1982) to investigate the convergence of the distribution of the risk reserve process under the improbable event that v(u) is finite as u tends to infinity. This is joint work with Giacomo Mazzola. In the case of a heavy-tailed distribution of the claims, related results have been obtained by Asmussen and Klüppelberg (1996).
15.10 - 15.50 Coffee Break (Main Hall, F-Floor, Uhrenhalle)
15.50 - 16.30 Dr. Valerie Chavez-Demoulin (NCCR FINRISK, Dept. of Math., ETHZ)
Estimating Value-at-Risk for Financial Time Series: An Approach Combining Self-Exciting Processes and Extreme Value Theory

Abstract: Independence of widely separated extremes of financial time series seems reasonable in most applications but they almost always display short-range dependence in which clusters of extremes occur together. A pragmatic way of modelling extremes of a stationary process is to decluster the data and then apply the standard threshold excess model to the maxima only. One of the disadvantages of the declustering is that the opportunity to model within cluster behaviour is lost.
     Our approach aims to model the behaviour of the cumulative effect of the extreme values. We introduce a marked point process combining self-exciting processes for the exceedances with a time-dependent process for the threshold excesses of stationary financial time series. The form of the process allows realistic models in which recent events affect the current intensity more than more distant ones, but it also allows the intensity to depend on the sizes (marks) of the events. Estimates of Value-at-Risk are derived for real data sets and backtested. (Joint work with A. C. Davison and A. J. McNeil.)

General Information

Participation is free, and there is no official registration. Everyone is welcome, practitioners are especially encouraged to attend. We have not made any special arrangements for lunch since there are sufficient possibilities nearby, in particular at ETH and the University. There is also the Dozentenfoyer. For hotel accommodation, please check the Zürich Tourism home page. Some of the hotels are nearby.

Local Organizer: PD Dr. Uwe Schmock (Director MAS Finance Program, ISB)

Conference Secretary: Ms. Irma Drack, CLP D4 (IFOR), Phone 01/632 40 16, E-mail: drack@ifor.math.ethz.ch

Other Risk Days: 1998, 1999, 2000, 2001, 2003, 2004

Please send comments and suggestions concerning this page to Uwe Schmock, e-mail: schmock@math.ethz.ch
Last update: September 4, 2003