Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Ralf Korn
University of Kaiserslautern
Recent Advances in Option Pricing with Binomial Trees
Binomial trees are used in option pricing for over 30 years. However, their irregular convergence and
problems with multi-dimensional trees still call for research. In the talk, we will present the so-called
optimal drift method to speed up the convergence of approximating binomial trees in the univariate
setting by generalizing results by Chang and Palmer. Further, we introduce the orthogonal decomposition
method to construct regular multivariate trees that can be applied universally for valueing options on
multiple assets.
Jan H. Maruhn
UniCredit, München
Exploiting GPUs and Adjoints for Rapid Monte Carlo Calibrations
Due to performance constraints the class of Equity models used in the front office has often been
limited to models with closed form solution for plain vanilla options, or models with on-the-fly calibration
(like the Dupire local volatility model). In this talk we will show that recent developments on the hardware
and algorithm side allow to break this paradigm. By combining the speedup of GPUs, adjoints
and multi-layer techniques, the Monte Carlo calibration of financial market models has become feasible
for large scale purposes - thus allowing to choose models based on their dynamics, and not their feasibility.
Kees Oosterlee
Techische Universität Delft
Efficient valuation methods for contracts in finance and insurance
In this presentation we will discuss the use of Fourier cosine expansions for pricing financial and
insurance derivative contracts. We will discuss hybrid SDE models, like the Heston Hull-White model,
modelling for example inflation options, and stochastic control problems.
Christoph Winter
Eidgenössische Technische Hochschule Zürich (ETHZ)
Wavelet Galerkin schemes for option pricing in multidimensional Lévy models
We consider a wavelet Galerkin scheme for solving partial integrodifferential equations arising from option
pricing in multidimensional Lévy models. Sparse tensor product spaces are applied for the discretization
to reduce the complexity in the number of degrees of freedom and wavelet compression methods are
used to decrease the number of non-zero matrix entries. We give numerical examples. In particular,
the regularization of the multidimensional Lévy measure is considered where small jumps are either
neglected or approximated by an artificial Brownian motion.
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