ETH Zurich


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

RiskLab, ETH Zürich

Location: ETH Zürich, Main Building, Lecture Hall HG E7

Time: Friday, October 20, 2000, 8.50-17.30

Conference program and abstracts are available online:


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. We look at the implications of such models under the assumption that the shock processes are Poisson, consider the modelling of dependent severities and give examples of the usefulness of these ideas in insurance and credit risk modelling.
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 d-dimensional 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, F-Floor, Uhrenhalle)
11.00 - 11.30 Dr. Thorsten Rheinländer (Dept. of Math., ETH Zürich)
Risk-Minimizing Hedging Strategies

Abstract: It is in general not possible to replicate the payoff of some stochastic liability by following a self-financing trading strategy after some initial investment. Typical examples include unit-linked 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 mean-variance 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/bfUniversity 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 2-factor CIR-model 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 square-root diffusion process with a modification that allows for the default process to be correlated with the factors driving the default-free 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. We introduce a second (correlated) log Brownian asset into the well known Merton investment model, on which no trading is allowed. However, the investor receives some of the untraded asset and the question is how to price and hedge this random payoff. Such frictions mean we are in the situation of incomplete markets. We propose an approximation to the solution for the 'optimal' price and hedge which is accurate when the position is small in comparison to wealth. Logarithmic utility is considered as a special case.
14.10 - 14.50 Roger Kaufmann and Pierre Patie (RiskLab, Dept. of Math., ETH Zürich)
Overview and Comparisons of Long-Term 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 long-term 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. The long-term goal of this RiskLab project is the development of a theoretically well-understood and empirically founded conceptual framework for the measurement of long-term financial risk of strategic investment portfolios. In this talk we primarily give an overview on models proposed for modelling the evolution of stochastic risk factors. Then, we present statistical techniques to estimate model parameters. Finally, after having defined a methodology which gives the effectiveness of each model, we provide comparison results obtained so far. The slides are available online.
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 risk-free short rate, and the credit spread composed of hazard rate and recovery rates, are affine functions of a set of state variables following jump-diffusion 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, F-Floor, Uhrenhalle)
16.00 - 16.30 Zheng Ziyu (RiskLab, Dept. of Math., ETH Zürich and INRIA Sophia-Antipolis, France)
Quality of Value-at-Risk Approximations by Numerical Solutions of SDEs

Abstract: This talk is focused on the measurement of the model risk for interest-rate 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. The slides are available online.
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 so-called 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. The prize is awarded to Dr. Damir Filipovic for his Ph.D. thesis Consistency Problems for HJM Interest Rate Models. Laudatory speech by Prof. Dr. Freddy Delbaen. The Chorafas Foundation awards prizes to Ph.D. students for exceptional work with practical relevance in the areas
  • Advanced technology - particulary communications, computers and sophisticated software,
  • New financial instruments, risk management systems, and financial modelling,
  • Birth control and environmental protection.

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: Dr. Uwe Schmock (RiskLab Research Director)

Conference Secretary: Ms Gerda Schacher,

Other Risk Days: 1998, 1999, 2001, 2002, 2003, 2004

Please send comments and suggestions concerning this page to Uwe Schmock, e-mail:
Last update: September 2, 2003