8.50  9.10  Prof. Dr. Freddy Delbaen
(Dept. of Math. and
RiskLab,
ETH Zürich) Welcome and Presentation of RiskLab Abstract: We give a short overview of the activities in Financial and Insurance Mathematics in Zurich, in particular the education in financial mathematics and the first year of the finance competence centre RiskLab at ETH Zurich. 
9.10  9.30  Dr. Uwe Schmock
(RiskLab,
Dept. of Math.,
ETH Zürich) Modelling Dependent Credit Risks with Beta Mixture Models Abstract: We model the number of defaults in a credit portfolio by first forming homogeneous groups characterized by their credit rating. Given a group's default probability, the individual defaults of its members are independent Bernoulli. The default probabilities of the groups are modelled using independent beta distributed random variables in such a way that strict monotonicity according to credit rating is preserved. This introduces a hierarchical dependence structure. A special feature of the model is the fact that it can be easily fitted to Standard & Poor's data, for example. 
9.30  10.00  Filip Lindskog
(RiskLab,
Dept. of Math.,
ETH Zürich)
Common Poisson Shock Models: Applications to Insurance and Credit Risk Modelling Abstract: Suppose we are interested in losses of different types and in the number and sizes of these losses that may occur over a given time horizon. A natural approach to modelling dependence between the frequencies of losses of different types is to assume that all losses can be related to a series of underlying and independent shock processes, but that a shock may cause losses of different types. 
10.00  10.30  Dr. Jeffrey F. Collamore
(RiskLab,
Dept. of Math.,
ETH Zürich) Ruin for Multidimensional Risk Processes Abstract: In the classical ruin problem, an insurance company gains capital from premiums income and loses capital as a result of claims; estimates are then given for the probability that the company's total capital is ever < 0, i.e., the probability that the company ever incurs ruin. In this talk, a multidimensional extension of the ruin problem will be discussed. In an applied setting, this could describe the probability that a quite general insurance or financial model of d > 1 (dependent) capital factors ever attains some "forbidden region" in ddimensional Euclidean space. Ruin estimates for this multidimensional problem will be given. An extension to a more general economic environment, where excess capital is actually invested, will be briefly sketched. 
10.30  11.00  Coffee Break (Main Hall, FFloor, Uhrenhalle) 
11.00  11.30  Dr. Thorsten Rheinländer
(Dept. of Math.,
ETH Zürich) RiskMinimizing Hedging Strategies Abstract: It is in general not possible to replicate the payoff of some stochastic liability by following a selffinancing trading strategy after some initial investment. Typical examples include unitlinked life insurance contracts or derivatives on risky assets with stochastic volatility. Therefore it is desirable to minimize the intrinsic risk according to some optimality criterion. We discuss several approaches like meanvariance and exponential hedging and provide a link to optimal martingale measures. 
11.30  12.00  Jacqueline Henn
(RiskLab,
Dept. of Math.,
ETH Zürich
and s/bf, University of St. Gallen)
Investigation of the Market Price of Credit Risk for the Swiss Bond Market Abstract: Credit risk plays an important role in the valuation and risk management of most financial contracts. This leads to great interest in problems of valuing credit risk  from a theoretical and practical point of view. We want to examine how well the model of Duffie and Singleton (1995, 1997) describes corporate bond yields for the Swiss bond market and how the spread can be separated into the expected and unexpected loss. The risk free term structure on the basis of Swiss treasury bonds is modelled with a 2factor CIRmodel where the model parameters are estimated with a Kalman filter. Based on these results we estimate the instantaneous probability of default for some Swiss corporations, which follows a translated single factor squareroot diffusion process with a modification that allows for the default process to be correlated with the factors driving the defaultfree term structure. Again the parameter estimations are done with a Kalman filter. 
12.00  13.40  Lunch Break 
13.40  14.10  Dr. Vicky Henderson
(Warwick Business School,
University of Warwick,
former member of RiskLab,
Dept. of Math.,
ETH Zürich) Real Options with Constant Relative Risk Aversion Abstract: Real options problems have recently attracted much attention worldwide and solutions are vital for many large international companies. One such problem is how to deal with claims on 'untraded' assets  often it is assumed that there is another similar traded asset and the two are correlated. In practice this traded asset might be used as a proxy and hedging done with this asset. Thus some notion of an 'optimal' hedge with this traded asset is needed. 
14.10  14.50  Roger Kaufmann
and
Pierre Patie
(RiskLab,
Dept. of Math.,
ETH Zürich) Overview and Comparisons of LongTerm Financial Risk Models Abstract: The assets managed by Switzerland's large institutional investors are huge. It is hence very important to have reliable measures of risk for these portfolios. The development of a methodology that could be used for the measurement of strategic longterm financial risks is therefore an important task. Existing modelling instruments such as RiskMetrics allow a relatively good measurement of market risks of trading books. These models, however, have some severe deficiencies if they are applied to longer time periods (typically one year), as is needed in the case of strategic investments of institutional investors. 
14.50  15.20  Aydin Akgün
(RiskLab,
Dept. of Math.,
ETH Zürich
and Swiss Banking Institute,
University of Zürich) Model Risk in Defaultable Security Valuation Abstract: The aim of the talk is to analyse the effects of different model specifications, within a general nested framework, on the valuation of defaultable bonds, defaultable options, and some credit derivatives. Assuming that the primitive variables, such as the riskfree short rate, and the credit spread composed of hazard rate and recovery rates, are affine functions of a set of state variables following jumpdiffusion processes, efficient numerical solutions for the prices of several defaultable securities are provided. The framework is flexible enough to permit some degree of freedom in specifying the interrelation among the primitive variables. This is crucial in that it is possible to see the pricing effects of the interaction between market and credit risk. It also allows a richer economic interpretation for the default process. 
15.20  16.00  Coffee Break (Main Hall, FFloor, Uhrenhalle) 
16.00  16.30  Zheng Ziyu
(RiskLab,
Dept. of Math.,
ETH Zürich and
INRIA SophiaAntipolis, France) Quality of ValueatRisk Approximations by Numerical Solutions of SDEs Abstract: This talk is focused on the measurement of the model risk for interestrate based European options. We analyse a Monte Carlo algorithm to compute quantiles of the law at time T of a diffusion process which is the solution to a stochastic differential equation. The global error results from a statistical error, which is governed by the number of samples, and a discretization error, which is governed by the stepsize for the Euler scheme used to discretize the stochastic differential equation. We give precise estimates on the discretization error and the statistical error. A typical example of the application is the numerical computation of the quantiles of the Profit and Loss of a misspecified hedging strategy. We show how our theoretical results can be applied to choose the numerical parameters of the simulation (number of samples, discretization step size) in order to obtain the desired accuracy on the quantiles. 
16.30  16.50  Prof. Dr. Rüdiger Frey
(Swiss Banking Institute,
University of Zürich) Modelling Dependent Defaults Abstract: We consider the modelling of dependent defaults. We focus in particular on socalled latent variable models such as KMV and CreditMetrics. We explore the role of copulas in modelling dependent default and present results from a simulation study, which shows that the way dependency among defaults is modelled can have a large effect on the distribution of credit losses. This is joint work with Dr. Alexander McNeil and Mark Nyfeler. 
17.00  Awarding of the Prize of the Dimitris N. Chorafas Foundation
by Prof. Dr. Guido Mislin
(Chairman of the Department of Mathematics)
in the presence of
Dr.h.c. Heinrich Steinmann
representing the Chorafas Foundation and
Prof. Dr. Gerhard Schmitt,
Vice President Planning and Logistics,
representing ETH Zürich.

Local Organizer: Dr. Uwe Schmock (RiskLab Research Director)
Conference Secretary: Ms Gerda Schacher,
Other Risk Days: 1998, 1999, 2001, 2002, 2003, 2004