[VFN] Financial and Insurance Mathematics at ETH Zurich (fwd)

Risk Day 2001 ------------- Mini-Conference on Risk Management in Finance and Insurance organised by RiskLab, ETH Zurich. Printable and online program with links: http://www.math.ethz.ch/finance/Risk-Day-2001.html Time: Friday, October 19, 2001, 9.00 - 17.30 Location: ETH Zurich, Main Building, Lecture Hall HG F7; Refreshments in the "Uhrenhalle" (main hall, F-floor) General Information: Participation is free, and there is no official registration. Everyone is welcome, practitioners are especially encouraged to attend. Program: -------- 9.00 - 9.10 Prof. Dr. Hans-Jakob Lüthi (IFOR and RiskLab, ETH Zürich) "Welcome and Presentation of RiskLab" 9.10 - 9.50 PD Dr. Wolfgang Breymann (RiskLab, Dept. of Math., ETH Zürich) "Volatility Estimation and Risk Measurement: Abstract: Market risk management, portfolio optimization and option pricing methods can only be as good as the model of the underlying volatility process. An approach will be presented that uses intraday high-frequency financial data to improve risk measurement at long time horizons. It takes advantage of the fact that volatility estimation on a time horizon of the order of days can be improved by the use of intra-day data. Such data require special methods for data analysis. The following results will be presented: - Universal method for deseasonalization of financial time series. - Use of intra-day data to improve volatility estimates at daily or longer time horizons. - Modelling financial time series by means of a hierarchical volatility model containing a cascade from long to short time horizons. An outlook will be given on how to use these techniques for portfolio optimisation and risk management at longer time horizons. 9.50 - 10.30 Enrico De Giorgi (RiskLab, Dept. of Math., ETH Zürich) "An Intensity Based Non-Parametric Default Model for Residential Mortgage Portfolios" Abstract: In December 2000 Swiss banks held about 505 billion CHF debts in the form of mortgages. Nonetheless, current models for credit risk are not designed to capture the specific dependence characteristics of a large mortgage portfolio. Given the huge size of the mortgage market, it is surprising that the issue has been largely ignored by academic research. Our attention lies in a proper way of modeling default risk for individual residential mortgages, which is affected by macro-economic factors such as unemployment, mortgage and factors specific to the obligor. We consider the time to default, using a non-parametric proportional hazard model for the intensity process, which is assumed to depend on a set of factors (macro-economic, mortgage and obligor specific). A technique from generalized additive models is used for estimation and the contribution of each factor to the default intensity is computed. 10.30 - 11.00 Coffee Break (Main Hall, F-Floor, Uhrenhalle) 11.00 - 11.30 Filip Lindskog (RiskLab, Dept. of Math., ETH Zürich) "Multivariate Extremes, Aggregation and Dependence in Elliptical Distributions" Abstract: The class of elliptical distributions provides a rich source of multivariate distributions which share many of the tractable properties of the multivariate normal distribution and enables modelling of multivariate extremes and other forms of non-normal dependences. In this talk I aim to clarify dependence properties of elliptical distributions and give examples how these results can be applied. (Joint work with Henrik Hult.) 11.30 - 12.00 Alessandro Juri (Dept. of Math., ETH Zürich) "Using Copulae to Bound the Value-at-Risk for Functions of Dependent Risks" Abstract: The theory of copulae is known to provide a useful tool for modelling dependence in integrated risk management. For given risks X_1,...,X_n and a real-valued functional f on R^n, bounds for the Value-at-Risk of the global position f(X_1,...,X_n) are provided. The key point is that we do not have specific dependence information on X_1,...,X_n. A further issue is how these bounds change when specific dependence information is assumed. Various examples highlight the methodology introduced. (Joint work with Andrea Höing and Prof. P. Embrechts.) 12.00 - 13.40 Lunch Break 13.40 - 14.10 Pierre Patie (RiskLab, Dept. of Math., ETH Zürich) "Risk Management for Derivatives in Illiquid Markets" Abstract: In this talk, we study the hedging of derivatives in illiquid markets. We consider a model where the implementation of a hedging strategy affects the price of the underlying security. We derive a formula for the feedback effect of dynamic hedging on market volatility and characterize perfect hedging strategies by a nonlinear version of the Black-Scholes PDE. Then we extend our approach to portfolios of derivatives by providing a pricing rule for the individual claims in a portfolio assuming that we know the overall hedge cost and the replicating strategy for the large trader. We solve numerically the PDE and we provide results (option prices and greeks) for different kinds of options. On the topic of risk management, we suggest a methodology to measure liquidity based on the estimation of implied parameters obtained from real option prices. Finally, simulations are used to assess the performance of various hedging strategies under market illiquidity. (Joint work with Prof. Rüdiger Frey, ISB, University of Zurich.) 14.10 - 14.40 Dr. Jesper Lund Pedersen (RiskLab, Dept. of Math., ETH Zürich) "An Optimal Selling Strategy Based on Predicting the Ultimate Maximum Price" Abstract: In this talk I will present an optimal selling strategy for an asset in the following sense: An investor with a long position in one asset decides to close the position before a given time. The investor continuously observes the asset price performance and has to determine the point in time (selling strategy) to close out the position so that the asset price is as close as possible to the ultimate maximum price over the given period. The probable proximity is measured by a probability distance. Thus, the investor's objective is to maximize, over all strategies, the probability that the asset price when the position is closed out is greater than a given percentage of the ultimate maximum price. 14.40 - 15.10 Dr. Larbi Alili (Dept. of Math., ETH Zürich) "Exponential Functionals of Brownian Motion and Asian Options" Abstract: Exponential functionals of Brownian motion play an important role in the valuation and hedging of Asian options. The aim of this talk is to provide an elementary method for computing the distribution of the latter functionals. 15.10 - 15.50 Coffee Break (Main Hall, F-Floor, Uhrenhalle) 15.50 - 16.20 Dr. Dirk Tasche (RiskLab, Dept. of Math., ETH Zürich) "Expected Shortfall and Beyond" Abstract: Expected Shortfall (ES) in several variants has been proposed as a remedy for the deficiencies of Value-at-Risk (VaR), which in general is not a coherent risk measure. In fact, most definitions of ES lead to the same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case even the coherence property of ES can be lost. The relations between some of the definitions of ES will be discussed. It will be pointed out that there is one which is robust in the sense of yielding a coherent risk measure regardless of the underlying distributions. In contrast to VaR, this variant of ES can always be estimated naively. Moreover, as shown recently by S. Kusuoka, it generates in a certain sense the class of all law invariant coherent risk measures. 16.20 - 16:50 Prof. Dr. Philippe Artzner (RiskLab and Université Louis Pasteur) "Coherent Acceptability for Multiperiod Risk and Applications" Abstract: We explain why and how to deal with the definition, the acceptability and the management of risk in a genuinely multitemporal way. Acceptable value processes are primitive objects and the measure of risk of a value process is the initial extra capital which makes it acceptable. Coherence axioms then provide a representation of a risk-adjusted valuation as the minimum expected value of an Stieltjes integral with respect to random measures. Some special cases allowing for recursive computations are presented. (Joint work with Freddy Delbaen, Jean-Marc Eber, David Heath and Hyejin Ku.) 17.00 Awarding of the Prize of the Dimitris N. Chorafas Foundation. Conference Secretary: Mrs G. Baltes, HG G37.2, Phone 01/632 34 00, E-mail: baltes(a)math.ethz.ch With best regards, Uwe Schmock Home Page: http://www.math.ethz.ch/~schmock/ Financial and Insurance Mathematics: http://www.math.ethz.ch/finance/ RiskLab: http://www.risklab.ch/