Activities
VIF Brown Bag Seminar (Wednesday, 14:00-15:00, SR 5th Floor)
The VIF Brown Bag Seminar is a platform where associated and visiting researchers talk
about their ongoing research. The meeting is informal and results may be preliminary.
Upcoming talks
Past talks
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September, 24th
Speaker: Andrea Macrina (King's College London & Kyoto University)
Talk: "Heat Kernel Models for Information-Sensitive Interest Rates"
Abstract: We propose a framework for the dynamics of the pricing kernel based on a heat kernel
approach under incomplete information. A so-called propagator is introduced that we
define by a function of time and the information about economic factors which is
available to market participants. The partial market information is modelled by a wide
class of continuous time-inhomogeneous Markov processes which may also include jumps. The
constructed pricing kernel models are used to price discount bonds and interest rate
derivatives in closed form. We then consider pricing kernels for multivariate assets.
Here partial information may also be modelled by time-inhomogeneous Markov processes with
different distributions. The multivariate models produce naturally correlated asset
prices which include stochastic interest rates in their dynamics.
(Joint work with Jiro
Akahori, Ritsumeikan University)
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August, 27th
Speaker: Thorsten Schmidt (Technical
University of Chemnitz, Germany)
Talk: "Market Models for CDOs with Statistics in View"
Abstract: The credit crisis showed the importance of sophisticated modelling of
credit portfolio products. Our starting point is the dynamic modelling of collateralized
debt obligations from Filipovic, Overbeck and Schmidt (2009). However, we assume that
only CDOs with certain maturities are traded and analyse conditions for absence of
arbitrage and the pricing of derivatives. As market data consists only of CDOs for a
fixed number of maturities, this step is crucial for statistics and calibration.
This is joint work with Zorana Grbac.
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July, 15th
Speaker: Tom Hurd (McMaster University, Canada)
Talk: "Structural models for credit and equity"
Abstract: We extend the structural credit modelling approach of Black and Cox to a unification of
equity products (written on the stock price) and credit products like bonds and credit
default swaps (CDS). This ``hybrid'' model and its extensions involving time-changed
Brownian motions are capable of reproducing well known equity models such as the variance
gamma model, at the same time producing the stylized facts about default stemming from
structural models of credit.
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June, 25th
Speaker: Markus Riedle (University of Manchester)
Talk: "Cylindrical Wiener and Lévy processes"
Abstract:
Cylindrical Wiener processes are a well known and often used source of random
noise for models in infinite dimensional spaces. In this talk we use the
classical theory of cylindrical processes and cylindrical measures to define
cylindrical Wiener processes and we relate this approach to the more common
definitions in literature. Once we have seen the charm of this
approach we define analogously cylindrical Lévy processes.
The cylindrical approach allows a straightforward definition of a stochastic
integral in both cases of a cylindrical Wiener and cylindrical Lévy process
without any geometric constraints on the underlying Banach space. We use this
integral to develop a theory of cylindrical differential equations and
demonstrate its practicalness by presenting some basic facts on the cylindrical
Ornstein-Uhlenbeck process driven by a cylindrical Lévy process.
(This is joint work with Dave Applebaum)
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May, 27th
Speaker: Emanuela Rosazza Gianin
Talk: "Representation of the penalty term of dynamic time-consistent convex risk measures"
(joint work with F. Delbaen and S. Peng)
Abstract:
Starting from the well known representation of dynamic convex risk measures, in a
Brownian setting with finite horizon we will provide a characterization of the penalty
functional in such a representation.
More precisely, such a characterization is deduced by applying the theory of Backward
Stochastic Differential Equations (in particular, of the so called g-expectations) and by
the fact that the minimal penalty term admits a càdlàg modification.
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May, 20th
Speaker: Michael Kupper
Talk: "Quasi-Convex Risk Measures"
Abstract: We study complete quasi-convex duality theory in the spirit of
Cerreia et al.. As an application, a dual representation result for
quasi-convex risk measures is given. The results are illustrated by several
examples. It is based on joint work with Samuel Drapeau.
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April, 29th
Speakers: Ronald Hochreiter and David Wozabal (University of Vienna)
Talk: "A Coupled Markov Chain Approach to Risk Analysis of Credit Default Swap Index Products"
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April, 22nd
Speaker: Vilimir Yordanov
Talk: "Dynamic CDO modeling"
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February, 25th
Speaker: Gregor Svindland
Talk: "Optimal Risk Sharing with
Different Reference Probabilities"
Abstract: We investigate the problem of optimal risk sharing between
agents endowed with cash-invariant choice functions which are
law-invariant with respect to different reference probability measures.
We motivate a discrete setting both from an operational and a
theoretical point of view, and give sufficient conditions for the
existence of Pareto optimal allocations in this framework. Our results
are illustrated by several examples.
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February, 4th
Speaker: Nicolas Vogelpoth
Talk: "Approaches to Conditional Risk"
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December, 10th
Speaker: Robert Stelzer
Talk: "Multivariate Levy driven Stochastic Volatility Models - OU type and COGARCH"
Abstract: Multivariate extensions of two continuous time stochastic volatility models driven by Levy processes -
the Ornstein-Uhlenbeck type and the COGARCH model - are introduced.
First, Ornstein-Uhlenbeck type processes taking values in the positive semi-definite matrices
are defined using matrix subordinators (special matrix-valued Levy processes) and a special
class of linear operators. Naturally these processes can be used to describe the random evolvement
of a covariance matrix over time and we therefore use them in order to define a multivariate
stochastic volatility model for financial data which generalises the popular univariate model
introduced by Barndorff-Nielsen and Shephard. For this model we show that the conditional
characteristic function can be calculated explicitly and is affine in the initial values,
which illustrates that the model is affine with the state space being the product of the
d-dimensional Euclidean space and the positive semi-definite matrices. Moreover, we derive
results regarding the second order structure, especially regarding the returns and squared
returns, which leads to a GMM estimation scheme. Finally, we discuss extensions allowing to model long memory phenomena.
Thereafter, an alternative stochastic volatility model driven only by a single d-dimensional Lévy process
- the multivariate COGARCH process - is introduced and analysed. After giving conditions for the finiteness
of moments and the existence of stationary distributions for the volatility process, we establish asymptotic
second order stationarity and show that the log-returns over consecutive intervals of the same length have the
autocovariance structure of an ARMA(1,1) process.
- November, 12th
Speaker: Samuel Drapeau
Talk: "Conditional Robust Utility Representation",
Abstract: "Many problems arise when looking at dynamic risk measures or
utility optimization concerning the intertemporal consistency
behavior. We will first look at some results enlightening this
problematic. Then, in order to get a better insight, we will come back
to the axiomatic level of preference orders and their related robust
representation in a dynamic setting."
- (Monday) October, 20th (14:00, Seminar Room 4)
Speaker: Mike Ludkovski
Talk: "Optimal Risk Sharing under Distorted Probabilities",
Abstract: "We study optimal risk sharing among n agents endowed with distortion
risk measures. Our model includes market frictions that can either
represent linear transaction costs or risk premia charged by a
clearing house for the agents. Risk sharing under third-party
constraints is also considered. We obtain an explicit formula for
Pareto optimal allocations. In particular, we find that a stop-loss or
deductible risk sharing is optimal in the case of two agents and
several common distortion functions. This extends recent result of
Jouini et al. (2006) to the problem with unbounded risks and market
frictions. This is joint work with Jenny Young (U of Michigan)."
- September, 24th
Speaker: Barbara Rüdiger
Talk: "Existence and uniqueness of solutions of infinite dimensional stochastic differential
equations".
- August, 6th
Speaker: Eberhard Mayerhofer
Talk: "Order preserving semi-flows",
Abstract: "We discuss well known theorems characterizing order preserving semi-flows on
convex subset of n-dimensional euclidean space."
- July, 2nd
Speaker: Gregor Svindland
Talk: "Sigma-additive equilibrium pricing rules for law-invariant convex risk measures".
- June, 25th
Speaker: Eberhard Mayerhofer (jointly with Christa Cuchiero)
Talk: "Affine processes with matrix state-space",
- June, 4th
Speaker: Eberhard Mayerhofer
Talk: "Simplifying diffusion functions of affine processes",
Abstract: "We characterize the Dai-Singleton class of affine models within the general affine framework (Duffie, Filipovic and Schachermayer)."
- (Thursday) May, 29th
Speaker: Andrea Macrina (King's College London)
Talk: "Dynamic Forward State Price Surfaces",
- May, 14th
Speaker: Damir Filipovic
Talk: "Dynamic CDO Term Structure Modelling", paper
- May, 7th
Speaker: Zehra Eksi
Talk: "Inflation Linked Derivatives: Pricing Model for a Multi-Country Setting"
- April 23rd
Speaker: Michael Kupper
Talk: "On Law Invariant Time Consistent Functions"
Abstract: We show that every dynamic risk measure which is law invariant and time
consistent is the entropic one. Moreover, every normalized, strictly monotone,
continuous, law invariant and time consistent function on the space of bounded random
variables is of the form u^{-1}(E[u(X)]) for some strictly increasing, continuous
function u. It is joint work with Walter Schachermayer.
- April 2nd
Speaker: Irina Slinko
Talk: "Joint term structures of nominal and real interest rates in a
two-country setting"
- March 5th
Speaker: Vilimir Yordanov
Talk: "Multicurrency Sovereign Bonds Arbitrage".
- February 27th
Speaker: Martin Keller-Ressel
Talk: "An alternative approach to affine processes and sufficient conditions for regularity"
Abstract: In this talk I will present some preliminary results from my current research.
The first part deals with an alternative proof for one of the main results of Duffie,
Filipovic & Schachermayer (2003) -- the characterization of a regular affine process in
terms of the admissible parameters. The proof should be especially appealing for people
familiar with Levy processes or infinite divisibility. In the second part of the talk
some sufficient conditions for regularity of an affine process are discussed.