Fakultät II Mathematik und Naturwissenschaften Institut für Mathematik

Forschungsseminar
Stochastische Analysis und Stochastik der Finanzmärkte

Bereich für Stochastik
P. BANK, D. BECHERER, H. FÖLLMER, P. FRIZ, U. HORST, P. IMKELLER, M. KELLER-RESSEL, U. KÜCHLER, M. KUPPER, A. PAPAPANTOLEON

Ort: TU Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Raum MA 041 im Erdgeschoß

Zeit: Donnerstag, 16 Uhr s.t.

Kaffee & Gebäck ab 15.45 Uhr s.t. im Raum MA 721

28. April 2011, 16 Uhr c.t.

Dr. Jörn Rank (d-fine GmbH, Partner), Thomas Pöche (d-fine GmbH, Berater) (Frankfurt/Main)

Risikomanagement-Beratung bei der d-fine GmbH: Ein Einblick in die Beratungspraxis am Beispiel Marktrisikomanagement

Abstract:
Ausgehend von einem Überblick über die mathematischen und aufsichtrechtlichen Grundlagen der Marktrisikomessung werden in dem Vortrag die verschiedenen, im Finanzsektor gebräuchlichen Verfahren zur Ermittlung des Marktrisikos angesprochen. Es werden die Vor- und Nachteile dieser Verfahren diskutiert sowie praktische Probleme erwähnt, die bei einem Umsetzungsprojekt zur Einführung einer Marktrisikomessung zu lösen sind. Der zweite Teil des Vortrages dient der Vorstellung der d-fine GmbH, einem der führenden europäischen Beratungsunternehmen, das sich auf strategische, quantitative und technische Fragestellungen im Risikomanagement spezialisiert hat. Hierbei wird insbesondere auf die typischen Aspekte eingegangen, die Studierende, Doktorandinnen und Doktoranden sowie Post Docs vor einem Wechsel in die außeruniversitäre Berufswelt besonders interessieren. Im Anschluss an den Vortrag besteht im Rahmen eines Umtrunks die Möglichkeit, mit den Vortragenden persönlich ins Gespräch zu kommen.

12. Mai 2011, 16 Uhr c.t.

Christa Cuchiero (ETH Zurich)

Affine Processes and Applications to Multivariate Stochastic Volatility Modeling

Abstract:
We give an overview of results on affine processes with general and conic state spaces, including path properties, regularity and admissibility conditions. Based on these results, we then consider a class of tractable multivariate stochastic volatility models, where the risk-neutral dynamics of the d-dimensional logarithmic price process and its instantaneous stochastic covariation process are described by an affine process with state space R^dxS^+_d. Here, S^+_d denotes the cone of positive semidefinite dxd matrices. This class contains for example the multivariate Heston model studied in [1] and a multivariate version of the Barndorff-Nielsen-Shepard model, which has been introduced in [2] under the name multivariate stochastic volatility model of OU-type. We here present necessary and sufficient conditions on the parameters describing the semimartingale characteristics of general affine stochastic volatility models such that the (discounted) price processes are martingales. In view of the practical applicability of such models, we also address the issue of model calibration. [1] J. Fonseca, M. Grasselli, and C. Tebaldi. Option pricing when correlations are stochastic: an analytical framework. Review of Derivatives Research, 10(2):151{180, 2007. [2] C. Pigorsch and R. Stelzer. A multivariate Ornstein-Uhlenbeck type stochastic volatility model. Working paper, Technical University Munich, 2009.

12. Mai 2011, 17 Uhr s.t.

Flavia Giammarino (London School of Economics)

Indifference Pricing with Uncertainty Averse Preferences

Abstract:
We consider the indifference valuation of an uncertain monetary payoff from the perspective of an uncertainty averse decision-maker. We study how the indifference valuation depends on the decision maker's attitudes toward uncertainty. We obtain a characterization of comparative uncertainty aversion and various characterizations of increasing, decreasing, and constant uncertainty aversion.

26. Mai 2011, 16 Uhr c.t.

Goran Peskir (University of Manchester)

A Duality Principle for the Legendre Transform

Abstract:
We present a duality principle for the Legendre transform that yields the shortest path between the graphs of functions and embodies the underlying Nash equilibrium. A useful feature of the algorithm for the shortest path obtained in this way is that its implementation has a local character in the sense that it is applicable at any point in the domain with no reference to calculations made earlier or elsewhere. The derived results are applied to optimal stopping games for Markov processes where the duality principle corresponds to the semiharmonic characterisation of the value function.

26. Mai 2011, 17 Uhr s.t.

Ingo Fahrner (Landesbank Baden-Württemberg)

Current Challenges in Interest Rate Modelling

Abstract:
In the first part of this talk we will review the development of interest rate models over the last 20 years. We will clearly see which problems arised and how they were attempted to be solved. We will also name the current issues since the 2007 financial crises. In a second and more mathematical part we will propose a new variant of the Linear Gauss Markov interest rate model addressing these issues.

9. Juni 2011, 16 Uhr c.t.

Kostas Kardaras (Boston University)

On Random Times

Abstract:
In this talk, a study of random times on filtered probability spaces is undertaken. One of the main messages is that, as long as distributional properties of adapted processes up to the random time are involved, there is no loss of generality in assuming that the random time is actually a randomized stopping time. This perspective sheds an intuitive light on results in the theory of progressive enlargement of filtrations, as is the semimartingale decomposition result of Jeulin and Yor. Financial applications of the previous theory include the role of the numeraire portfolio in stochastic finance as an indicator of overall market performance, as well as the problem of expected utility maximization from terminal wealth with a random time-horizon. Further applications in distributional properties of one-dimensional transient diffusions up to certain random times will be discussed.

9. Juni 2011, 17.00 Uhr s.t.

Jan Kallsen (Christian-Albrechts-Universität zu Kiel)

Models of HJM and LIBOR type for option prices

Abstract:
In the Heath-Jarrow-Morton (HJM) approach in interest rate theory the whole forward rate curve rather than the short rate is considered as state variable for a stochastic model. Absence of arbitrage then leads to consistency and drift restrictions, in particular the HJM drift condition. Models of LIBOR type proceed similarly, but focus instead on only finitely many bonds resp. simple forward rates. Several attempts have been made to transfer the HJM approach to options on a stock, e.g. by Schönbucher, Schweizer & Wissel, Carmona & Nadtochiy, Jacod & Protter. Here, the underlying stock plays the role of the short rate. The implied volatility surface or a reparametrisation serves as state variable and hence as counterpart of the forward rate curve in the classical framework of HJM. A "LIBOR-type" model for options with only finitely many maturities and strikes is considered by Wissel. In this talk we discuss general principles underlying - in our eyes - reasonable frameworks of HJM resp. LIBOR type. Moreover, we present appraoches to both questions which are based on using time-inhomogeneous Levy processes for parametrising call prices.

23. Juni 2011, 16 Uhr c.t.

Eberhard Mayerhofer (Vienna Institute of Finance)

On the validity of the affine transform formula in the presence of jumps

Abstract:
In this talk I address the topic of Fourier pricing in the context of multivariate affine jump-diffusion processes. A series of connected joint works with Damir Filipovic, Martin Keller-Ressel and other colleagues have lead to a deep understanding of the affine property. They allow to use the extended affine transform formula when pricing contingent claims with Fourier-inversion as put forward by Carr and Madan in their 99' paper.

23. Juni 2011, 17 Uhr s.t.

Julian Tugaut (Universität Bielefeld)

Convergence of a self-stabilizing diffusion

Abstract:
A self-stabilizing process corresponds to a particle in a mean-field random dynamical system whose the dimension is infinity. Benachour, Roynette and Vallois proved the weak convergence of this kind of processes. Cattiaux, Guillin and Malrieu extended this result by adding the gradient of a convex potential in the drift term. Carrillo, McCann and Villani proved a similar result in non-convex case by assuming the center of mass is fixed. By using the thirdness of the stationary measures and the free-energy functional, I will prove the convergence under simple conditions and discuss about the basins of attraction.

07. Juli 2011, 16 Uhr c.t.

Bruno Bouchard (Université Paris-Dauphine)

Stochastic Targets and Stochastic Targets with Controlled Loss: Recent Improvements

Abstract:
We review recent advances on stochastic target problems. In particular we explain how they are related to pricing and optimal management problem under risk constraint. Several examples of practical application will be discussed.

07. Juli 2011, 17 Uhr s.t.

Pavel Gapeev (London School of Economics)

Pricing of defaultable claims in dividend switching models with partial information

Abstract:
We study two models of financial markets in which the dividend rates of risky assets change their initial values to other constant ones at the times at which certain unobservable external events occur. In the first model, the price dynamics of two assets are described by geometric Brownian motions with random drift rates switching at exponential random times which are independent of each other and of the two constantly correlated driving Brownian motions. In the second model with credit risk, the price of a unique risky asset is described by a geometric Brownian motion and the default intensity rate is modeled by the square root process with random drift rates switching at subsequent exponential random times independent of the unique driving Brownian motion. We obtain closed form expressions for rational values of European contingent claims through the filtering estimates of the occurrence of switching times and their conditional probability density derived given the filtration generated by the underlying asset price processes. The presentation is based on joint work with Monique Jeanblanc (University of Evry).