FAM-ily  

Financial and Actuarial Mathematics  
TU Wien, Austria  

 

Vienna Science and Technology Fund (Wiener Wissenschafts-, Forschungs- und Technologiefonds - WWTF) Half-Day Workshop on
Credit Risk and Risk Transfer

sponsored by the Vienna Science and Technology Fund (WWTF)
through grant MA13 "Mathematics and Credit Risk"

Location: Vienna University of Technology, Freihaus Building, Wiedner Hauptstrasse 8-10, 1040 Vienna,
Lecture Theatre Freihaus Hörsaal FH3 (yellow area, 2nd floor)

Time: Wednesday, January 25, 2006, 2pm to 6pm

Program:

14:00-14:15 Prof. Dr. Uwe Schmock
(Financial and Actuarial Mathematics Group (FAM), Vienna University of Technology)
 
Welcome
 
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14:15-15:00 Prof. Dr. Walter Schachermayer
(Financial and Actuarial Mathematics Group (FAM), Vienna University of Technology)
 
Optimal Risk Sharing for Law Invariant Monetary Utility Functions
 
Abstract: We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions. We first prove existence of an optimal risk sharing allocation which is in addition increasing in terms of the total risk. We next provide an explicit characterization in the case where both agents' utility functions are comonotone. The general form of the optimal contracts turns out to be given by a sum of options (stop-loss contracts, in the language of insurance) on the total risk. In order to show the robustness of this type of contracts to more general utility functions, we introduce a new notion of strict risk aversion conditionally on lower tail events, which is typically satisfied by the semi-deviation and the entropic utility functions. Then, in the context of an AV@R-agent facing an agent with strict monotone preferences and exhibiting strict risk aversion conditional on lower tail events, we prove that optimal contracts again are European options on the total risk.
Joint work with E. Jouini (Université Paris Dauphine) and N. Touzi (CREST Paris and Imperial College London).
 
Download slides of the talk and find related papers [123] and [124] in Schachermayer's list of publications
15:00-15:45 Dipl.-Ing. Richard Warnung
(Financial and Actuarial Mathematics Group (FAM), Vienna University of Technology)
 
CreditRisk+ - General Extensions and Modelling of Correlations
 
Abstract: The CreditRisk+ methodology got broad acceptance due to its numerical stability and its ability to yield numerous extensions. In this talk I will first give an introduction to the classical framework and then introduce stochastic loss given default. Furthermore I especially want to present expected shortfall and risk contributions in this generalized framework. Finally I want to discuss the modelling of risk sector correlations respectively default correlations. This is work guided by Prof. Uwe Schmock initiated by two projects with the Austrian Central Bank.
 
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15:45-16:15 Coffee Break
16:15-16:45 Dr. Rainer Jankowitsch
Department of Finance and Accounting, Vienna University of Economics and Business Administration)
 
Explaining the Credit Default Swap Basis
 
Abstract: This paper aims at providing an explanation for the CDS basis, i.e. for the difference between quoted CDS spreads and bond spreads of the same issuer. We hypothesize that the delivery option embedded in CDS contracts accounts for the implied recovery parameter in the CDS market being less than the recovery parameter in the bond market. Both a cross-sectional analysis and individual time series analyses identified five significant factors influencing the implied CDS recovery rates through the delivery option premise, such as the creditworthiness of the corporation, the number of its bonds outstanding, their maturities and pricing errors. These empirical tests also provided evidence that the effect of the delivery option has indeed a sufficient magnitude to explain the size of the CDS basis.
Joint work of Rainer Jankowitsch, Rainer Pullirsch, and Tanja Veza.
 
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16:45-17:30 Dr. Josef Teichmann
(Financial and Actuarial Mathematics Group (FAM), Vienna University of Technology)
 
Adaptive Recombination for Cubature Methods
 
Abstract: By the results of T. Lyons and N. Victoir on cubature formulas on Wiener space and S. Kusuoka on the convergence of weak high-order schemes for SDEs one can construct deterministic trees approximating weakly solutions of SDEs. We show that - by introducing certain types of recombination - such trees get more feasible for numerical purposes. The recombinations stem on one hand from Gronwall-type estimates along trajectories, on the other hand from natural recombination structures in free nilpotent Lie groups due to the Bass-Milnor Theorem. Some numerical experiments and applications to financial mathematics are presented.
Joint work with Christian Schmeiser (University of Vienna) and Alexander Soreff (Vienna University of Technology).
 
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17:30-18:00 Prof. Dr. Stefan Pichler
Department of Finance and Accounting, Vienna University of Economics and Business Administration
 
Validation of Credit Rating Systems Using Multi-Rater Information
 
Abstract: We suggest a new framework for the use of multi-rater information in the validation of credit rating systems, applicable in any validation process where rating information from different sources is available. As our validation framework does not rely on historical default information, it appears to be particularly useful in situations where such information is inaccessible. We focus on the degree of similarity or - more generally - proximity of rating outcomes stemming from different sources and show that it is important to analyze three major aspects of proximity: agreement, association, and rating bias. We suggest using a weighted version of Cohen's kappa to measure the agreement between two rating systems and we introduce a new measure for rating bias. In contrast to the existing literature, we suggest a measure of association which is based on the Kemeny-Snell metric and, opposed to other measures, is consistent with a set of basic axioms and should therefore be used in the context of multi-rater information. We provide an illustrative empirical example using rating information stemming from the Austrian Credit Register on partially overlapping sets of customers of 27 banks. Using a multi-dimensional scaling technique in connection with a minimal spanning tree we show that it is possible to consistently detect "outliers", i.e., banks with a low degree of similarity to other banks. The results indicate that banks which are less diversified across the size of their loans are more likely to be outliers than others.
Joint work of Kurt Hornik, Rainer Jankowitsch, Manuel Lingo, Stefan Pichler, and Gerhard Winkler.
 
Download related paper to the talk


General Information

Participation is free, and there is no official registration - nevertheless we would be happy if you write - for administrative reasons - a short e-mail to our secretary Sandra.Trenovatz@fam.tuwien.ac.at with your name and university or company.
Everyone is welcome, practitioners are especially encouraged to attend.

We have not made any special arrangements for lunch since there are sufficient possibilities nearby ([Ms-Word/212kb], [PDF/135kb]).

For hotel accommodation, please check the Wien Tourism home page or a list of hotels near TU Wien.

Organizers:

Workshop Secretary: