(Actuarial Seminar,
organized by Swiss Re,
sponsered by Swiss Life.
Please send an e-mail to Peter Antal
if you intend to come.)
Friday, February 5, 1999, 15.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Albert N. Shiryaev
(Steklov Mathematical Institute, Moscow)
An extension of the distributional Paul Lévy theorem
with applications to the behaviour of financial prices
(Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, February 4, 1999, 17.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Abstract:
We present some mathematical tools used to compute the intensity of a
single jump process. We apply these results to the valorisation of a
contingent claim when default may appear. In the first part, we study the
case where the agent has no information except that he knows, at any
time t, if the default has or has not appeared. In particular, we
examine the Duffie-Lando model [2] and give a shorter proof of their main
result. In the second part, we study the case where the agent knows the
filtration of the default-free asset and the information of the time when
the default appears, as in the first part. We prove that the hypothesis of
Duffie-Schröder and Skiadias [1] stands only in particular cases which
include the Kusuoka model [3]. We end the talk with some questions and a
partial answer about the modelling of the information. (Joint work with
Robert J. Elliott) References:
D. Duffie, M. Schröder and C. Skiadias:
Recursive valuation
of defaultable securities and the timing of resolution of uncertainty.
The Annals of Prob., vol. 6, pp. 1075-1090, 1996.
D. Duffie and D. Lando:
Term structure of credit spreads with
incomplete accounting information, preprint, 1997.
Kusuoka:
Some remarks on default risk, preprint, 1998.
(Seminar for Financial and Insurance Mathematics, ETHZ)
Tuesday, February 2, 1999, 17.15 h
(ETHZ, HG D7.1)
Abstract:
We consider a general semimartingale model of a currency market with
transaction costs and establish a hedging theorem giving a dual
description of the set of initial endowments allowing to hedge a contingent
claim in various currencies by a self-financing portfolio.
(Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, January 14, 1999, 20.00 h (Restaurant "Au Premier",
Zürich Main Station)
Andreas Schlatter (UBS Brinson)
Measuring and handling of portfolio risk
(Actuarial Seminar,
organized by Swiss Re,
sponsered by Swiss Life.
Please send an e-mail to Peter Antal
if you intend to come.)
Thursday, January 14, 1999, 17.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Abstract:
The implied savings account introduced by Musiela/Rutkowski is a
generalization of the classical savings account. The main tool for our
analysis is the multiplicative decomposition of semimartingales under two
different equivalent probability measures. We prove the existence and
uniqueness of the implied savings account in a very general setting.
(Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, January 14, 1999, 12.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Abstract:
In many models dealing with price equilibrium, the offer and demand
are supposed to be given exogenously. But such models may not be very
useful when we try to explain the driving mechanisms of the price
evolution of an asset traded for example at the swix. We will discuss
some models where several agents observe and participate to the market
via an order book. Even for a quite "simplistic" behaviour of the
agents, the correspondig equilibrium price process has some "unexpected"
features.
(Informal Lunch-Time Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, December 17, 1998, 17.15 h
(ETHZ, HG G3)
Abstract:
When fitting data and pricing financial instruments, the choice of
the underlying model can significantly predetermine the corresponding results. This
model risk is illustrated by the
WinCAT coupons "Hail"
of the
Winterthur Insurance
convertible bond, where many different models are consistent with the
available historical data. The wide spectrum of different results arising from these
models is presented. For selected models, the consistency and the dispersion are
analyzed by simulation studies.
(Olsen & Associates inhouse seminars)
Thursday, December 10, 1998, 17.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Abstract:
We consider the problem of maximising the expected utility of terminal
wealth in the framework of a general incomplete semimartingale model of a
financial market. We show that the necessary and sufficient condition on
a utility function for the validity of several key assertions of the
theory to hold true is the requirement that the asymptotic elasticity
of the utility function is strictly less than one.
(Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, December 10, 1998, 12.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Abstract:
This talk will provide a conceptional insight into a thesis work about
optimized portfolio selection in (re)-insurance. The motivation is to
derive a consistent [...] risk measure taking into account both, risk and
return considerations subject to a competitive market environment. Such a
risk measure will serve a dual purpose. On the one hand it can be used as
premium indication in an absolute sense. On the other hand it will help us
in a relative fashion as hurdle rate criterion making explicit intrinsic
dangerosity on a risk specific basis and thus allowing for risk selection
subject to given market premiums. Of course the characterization of this
risk measure will prove to match observable market reality.
(Informal Lunch-Time Seminar for Financial and Insurance Mathematics, ETHZ)
Monday, December 7, 1998, 20.00 h (Restaurant "Au Premier",
Zürich Main Station)
(Actuarial Seminar,
organized by Swiss Re,
sponsered by Swiss Life.
Please send an e-mail to Peter Antal
if you intend to come.)
Thursday, December 3, 1998, 17.15 h
(ETHZ,
Hermann-Weyl-Zimmer, HG G43)
Abstract:
This talk gives a overview of two recent papers on backtesting
and maximum loss in the context of value-at-risk models. In the
first paper, we outline possible shortcomings of current
backtesting procedures, motivating the need for revised
backtesting methods. We propose new methods that are based on -
or closely related to - exceedances over a threshold. We compare
our proposal by a real-life example. In the second paper we
consider value at risk and maximum loss for linear portfolios.
The main results of the paper are related to the phenomenon of
fat tails, the normality assumption, stress tests, and the
application of factor three for capital requirements.
(Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, December 3, 1998, 16.15 h
(Hauptgebäude der Universität Zürich, Hörsaal E 18)
Abstract:
Nach einer allgemeinen Einführung in die Verbriefung von
Versicherungsrisiken wird das Beispiel der
WinCAT-Wandelanleihe
der Winterthur-Versicherung eingehend
erläutert. Für die Schätzung des Wertes der
WinCAT-Zinskupons "Hagel" steht eine Vielzahl von Modellen
zur Verfügung; insbesondere, wenn ein möglicherweise
vorhandener Trend in den Daten modellierbar sein soll.
Methoden der Extremwerttheorie kommen zur Anwendung. Für
ausgewählte Modelle werden die Robustheit, Konsistenz und
Dispersion mit Hilfe von Szenarien beziehungsweise
Simulationen untersucht.
Abstract:
This talk deals with the problem of pricing a financial
product relying on an index of reported claims
from catastrophe insurance. The problem of pricing such products is that,
at a fixed time in the trading period, we do not know
the total claim amount from the catastrophes occurred.
Therefore we have to price these products solely from knowing the
aggregate amount of the reported claims at the fixed time point.
This article will propose a way to handle this problem, and
will thereby extend the existing pricing models for products
of this kind. (Based on joint work with Hanspeter
Schmidli, 1998.)
(Seminar for Financial and Insurance Mathematics, ETHZ)
Wednesday, November 25, 1998, 14.30 h
(Hörsaal B1, Institut für Statistik, Universität Bern)
Abstract: We extend the definition of coherent risk measures, as
introduced by Artzner, Delbaen, Eber and Heath, to general probability
spaces and we show how to define such measures on the space of all random
variables. We also give examples that relates the theory of coherent risk
measures to game theory and to distorted probability measures. The
mathematics are based on the characterisation of closed convex sets of
probability measures that satisfy the property that every random variable is
integrable for at least one probability measure in this set.
(Swiss Probability Seminar, 16. meeting)
Thursday, November 19, 1998, 19.00 h (Restaurant "Au Premier",
Zürich Main Station)
Erwin Straub (Swiss
Re) Reminiszenzen eines Aktuars am ersten Tag seines Ruhestandes
(Actuarial
Seminar, organized by Swiss Re, sponsered by
Swiss Life.
Please send an e-mail to Peter Antal
if you intend to come.)
Thursday, November 19, 1998, 17.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
Abstract:
The problem of super-replication under transaction costs, in a
continuous-time Markov diffusion model, has been solved in the
one-dimensional case by means of a dual formulation of the problem. The
minimal super-replication cost is then given by the cost of the cheapest
buy-and-hold strategy. We provide an extension of this result to the
multivariate framework (as in Kabanov 1997), which can be seen as a
currency market. An important feature of the analysis is that the dual
formulation of the problem is not needed. Instead, we formulate a new
dynamic programming principle directly on the super-replication problem.
(Seminar for Financial and Insurance Mathematics, ETHZ)
Thursday, November 12, 1998, 12.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
Abstract:
We consider asset price models with stochastic "volatility" where the current value of the
"volatility" can be observed only partially. In particular we consider models where the
asset price process is given as exponential martingale of some doubly stochastic Poisson
process (a compound Poisson process where the intensity of the Poisson process
describing the number of jumps in the asset price is itself stochastic). We provide limit
results for large jump intensity and small jump variance relating these models to standard
continuous-time stochastic volatility models. We show how efficient nonlinear filtering
techniques can be employed to estimate the unknown volatility process. Finally we discuss
how our approach can be used for the computation of risk-minimizing hedging strategies
under restricted information.
(Informal Lunch-Time Seminar for Financial and Insurance Mathematics, ETHZ)
Friday, November 6, 1998, 14.00 h
(Olsen & Associates,
Seefeldstr. 233, Zürich, O-floor)
Abstract:
We propose a method for estimating VaR and related risk measures
describing the tail of the conditional distribution of a heteroscedastic financial
return series. Our approach combines quasi-maximum-likelihood fitting of GARCH
models to estimate the current volatility and extreme value theory for estimating
the tail of the innovation distribution of the GARCH model. We use our method
to estimate conditional quantiles (VaR) and conditional expected shortfalls (the
expected size of a return exceeding VaR). Using backtesting we show that our
procedure gives better estimates than methods which ignore the heavy tails of the
innovations or the stochastic nature of the volatility. With the help of our fitted
models and a simulation approach we estimate the conditional quantiles of returns
over multiple day horizons and find evidence of a power scaling law, where the power
depends in a natural way on the current volatility level.
(Olsen & Associates inhouse seminars)
Thursday, November 5, 1998, 17.15 h
(ETHZ, Hermann-Weyl-Zimmer, HG G43)
