Goethe Center for Scientific Computing (G-CSC)

Goethe University Frankfurt

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Financial Derivatives in Incomplete Markets

Project Description

FIDEUM: Modeling and Valuation of Financial Derivatives in Incomplete Markets

T. Gerstner with M. Griebel (Bonn), W. Jäger (Heidelberg), H.-J. Bungartz (München), C. Reiß (Berlin)

Industry Partners: DZ Bank, Thetaris GmbH

Funded by the BMBF program "Mathematics for Innovations in the Industrial and Service Sectors"

Incomplete markets require new statistical, analytical, and numerical methods, to cope, for example, with stochastic volatilities or jumps in the stochastic processes. These are investigated in a joint project of Heidelberg University (with focus on modeling and analysis), TU Berlin (with focus on statistics), Bonn University (with focus on numerics) and TU Munich (with focus on software development).

Goal of the numerical part of the joint project is the development of a sparse grid method for the solution of moderate-dimensional partial integro-differential equations and of Hamilton-Jacobi-Bellmann equations for the determination of optimal measures. To this end, a sparse grid solver is developed and implemented with which the differential as well as the integral operator is discretized in a wavelet basis. For the solution of the resulting sparse linear systems, parallel multigrid methods are employed.

The software which is developed in this project will be employed in cooperation with the project partners for the simulation and valuation of concrete and current financial products. After the evaluation phase, the programs can be utilized by all project partners.