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9.00–9.10 | Prof. Dr. Paul Embrechts
(Department of Mathematics,
ETH Zürich)Welcome and Introduction |

9.10–9.20 | Eckart Jäger
(NCCR FINRISK, ISB,
University of Zürich)Presentation of the Doctoral Program in Finance at the University of Zürich |

9.20–10.00 | Prof. Dr. Martin Schweizer
(Department of Mathematics,
ETH Zürich)Pricing and Hedging Recursive Payoff Structures Abstract:
We discuss some ideas in the context of pricing and hedging
financial structures whose payoffs are defined in terms of their
valuation—for instance defaultable bonds or certain insurance
products. This leads to a recursive definition of the value process
associated to such a structure, and we present a class of stochastic
models where such products can be handled by using PDE methods. This is
joint work with Dirk Becherer.
Discretizing these models also leads to
interesting new convergence problems, and we touch upon this issue as well. |

10.00–10.30 | Dr. Hansjörg Furrer
(RiskLab,
ETH Zürich)Quantifying Regulatory Capital for Operational Risk Abstract:
The proposed New Basel Capital Accord
(Basel II) established by the
Basel Committee on Banking Supervision
calls for an explicit treatment of operational risk. Banks are required to
demonstrate their ability to capture severe tail loss events. Value-at-risk is a risk
measure that could be used to derive the necessary regulatory capital. Yet operational
loss data typically exhibit irregularities which complicate the mathematical modeling.
It is shown that traditional modeling approaches, including extreme value theory, reach
their limits as the structure of operational loss data is barely in line with the
modeling assumptions. |

10.30–11.00 | Coffee Break (Main Hall, F-Floor, «Uhrenhalle») |

11.00–11.40 | PD Dr. Wolfgang Breymann
(RiskLab,
ETH Zürich)An Intraday Analysis of Diversified World Stock Indices Abstract:
This paper proposes an approach to the intraday analysis of diversified world
accumulation indices. The growth optimal portfolio (GOP) is used as reference
unit or benchmark in a continuous financial market model. Diversified global
portfolios, covering the world financial market, are constructed and shown to
approximate the GOP. The normalized GOP is modeled as a time transformed square
root process of dimension four. Its dynamics is empirically verified in a
robust manner for several world stock indices. Furthermore, the long-term
evolution of the transformed time is modeled via a constant net growth rate of the
drift of the discounted GOP and a quickly evolving market activity. The latter is
decomposed into a mean reverting stochastic market activity process and a
deterministic seasonal market activity component. The empirical findings identify
a simple and realistic model for a world stock index that reflects its historical
evolution reasonably well by using only a few constant parameters.
(Joint work with Leah Kelly and
Eckhard Platen) |

11.40–12.10 | Jonathan Wendin
(Department of Mathematics,
ETH Zürich)Generalized Linear Mixed Models in Portfolio Credit Risk Modelling Abstract:
A crucial point in portfolio credit risk modelling is that of dependence among default
events. One way of handling this is given by Generalized Linear Mixed Models (GLMMs); a
well-known concept in statistics for dealing with repeated measurements on different
units. This talk gives a general introduction to GLMMs with problems relating to
portfolio credit risk in mind. In this setting default probabilities or default
intensities are viewed as a result of both fixed effects and random
effects, where the latter are the key to dependence between counter-party defaults.
By choosing the random effects suitably we obtain dependence between defaults in a
given year as well as dependence between defaults in consecutive years—two kinds of
dependence that have been observed in empirical default data. |

12.10–13.50 | Lunch Break |

13.50–14.30 | Dr. Juri Hinz
(University of Tübingen,
starting Dec. 2003 at the
IFOR,
ETH Zürich)On Valuation of Electricity Contracts Abstract:
Beginning in the nineties a number of electricity markets have been deregulated. The
enforced competition in electricity production, retail, and trading raises various
problems concerning optimal market design, price risk management, and strategy
optimization. In this talk, we outline a special topic in this area elaborating on real
assets. The idea here is that, since electricity is not storable, the true underlying
will be the ability to produce power. Calculating equilibrium prices for production
capacites, we obtain a valuation of contracts which is fair in the sense that arbitrage
is excluded for capacity and claim trading. |

14.30–15.00 | Michael Kupper
(Department of Mathematics,
ETH Zürich)Coherent and Convex Risk Measure for càdlàg Processes Abstract:
If the random future evolution of values (such as the market value of a firm's equity,
the market value of a portfolio of financial securities or the surplus of an insurance
company) is modelled in continuous time, then a risk measure can be seen as a
functional on the space of stochastic processes. We extend the notions of coherent and
convex risk measures to the space of bounded càdlàg adapted processes.
We present
representation results based on convex duality theory and show that under a weak
continuity assumption (Fatou property) the representation holds in terms of
sigma-additive optional random measures. Furthermore, we discuss an extension to the
space of unbounded processes. As an example, we calculate the risk of a classical
Cramér–Lundberg process under a given coherent risk measure and compare it with
classical results. (Joint work with
Patrick Cheridito and
Freddy Delbaen) |

15.00–15.30 | Prof. Dr. Philipp Schönbucher
(Department of Mathematics,
ETH Zürich)Frailty Models, Contagion and Information Effects Abstract:
Most of the existing literature on default contagion
assumes a direct causal relationships between two obligors'
defaults. In contrast to this we show in this talk that
default contagion can also arise from information
effects if investors are imperfectly informed about
some common factors affecting the true riskiness of
the obligors. We model this effect in a simple
extension of the intensity-based modelling framework using
unobserved frailty variables. The default intensities in this
model exhibit jumps at default events of other obligors.
This entails much higher (and more realistic) levels of
default dependence between the obligors than what purely
diffusion-based intensity models were able to capture
previously, without adding too much additional complexity.
The parameters of the dependence can be implied directly
from spread jumps observed in the market, thus enabling
a full specification of the model under pricing probabilities
without recourse to historical default correlations. We
furthermore present two extensions of the model: The first
extension shows that the size of the contagion effect can
depend on the reason for the default and not just the identity
of the defaulted obligor, the second extension exhibits
stochastic default correlation. |

15.30–16.00 | Coffee Break (Main Hall, F-Floor, «Uhrenhalle») |

16.00–16.30 | Dr. Daniel Straumann
(starting Oct. 2003 at the
RiskLab,
Dept. of Math.,
ETH Zürich)Maximum Likelihood and Quasi Maximum Likelihood Estimation in Conditionally Heteroscedastic Time Series Models Abstract:
By exploiting the techniques of stochastic recurrence equations, we
develop a general and unifying limit theory for the maximum likelihood
estimator (MLE) and quasi maximum likelihood estimator (QMLE) in a
certain parametric class of conditionally heteroscedastic processes,
which contains widely used financial time series models:
(asymmetric) GARCH(1,1) and EGARCH. Our approach
generalizes and clarifies work of Lumsdaine (1996) and Berkes et
al. (2003). We furthermore discuss the issue of misspecification
in the MLE and the behavior of the QMLE in the presence of a
heavy-tailed noise distribution. This complements work
by Newey and Steigerwald (1997) and Hall and Yao (2003).
(The talk is based on my Ph.D. thesis) |

16.30–17.00 | Filip Lindskog
(RiskLab,
ETH Zürich)On Regular Variation for Stochastic Processes Abstract:
We study a formulation of regular variation on the space of
R^{d}-valued right-continuous functions on [0,1] with left limits
and provide necessary and sufficient conditions for a stochastic process with sample
paths in this space to be regularly varying. A version of the Continuous Mapping
Theorem is proved which enables the derivation of the tail behavior of rather general
mappings of the regularly varying stochastic process. For a wide class of Markov
processes with asymptotically independent increments we obtain simplified sufficient
conditions for regular variation. For such processes we show that the possible regular
variation limit measures concentrate on step functions with one step, from which we
conclude that extremes for such processes are due to one big jump in (0,1] or an
extreme starting point. Finally, using the Continuous Mapping Theorem we derive the
tail behavior of filtered regularly varying Markov processes with asymptotically
independent increments.
(Joint work with Henrik Hult) |

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.

- Prof. Dr. Uwe Schmock (Financial and Actuarial Mathematics, Vienna University of Technology)
- Prof. Dr. Philipp Schönbucher (Department of Mathematics, ETH Zürich)

**Other Risk Days:**
1998, 1999,
2000, 2001,
2002, 2004

Please send comments and suggestions to Uwe Schmock, email: schmock@math.ethz.ch. Last update: October 14, 2003 |