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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. An efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou's jumpdiffusion model
 Garcke, J.; Griebel, M.: Sparse grids and applications Berlin: Springer, 2013 (Lecture notes in computational science and engineering 88) ISBN: 3642317022 ISBN: 9783642317026 ISBN: 9783642317033 DOI: 10.1007/9783642317033 pp.121150 

 English 
 Book Article 
 Fraunhofer SCAI () 
Abstract
We use a sparse grid approach to discretize a multidimensional partial integrodifferential equation (PIDE) for the deterministic valuation of European put options on Kou's jumpdiffusion processes. We employ a generalized generating system to discretize the respective PIDE by the Galerkin approach and iteratively solve the resulting linear system. Here, we exploit a newly developed recurrence formula, which, together with an implementation of the unidirectional principle for nonlocal operators, allows us to evaluate the operator application in linear time. Furthermore, we exploit that the condition of the linear system is bounded independently of the number of unknowns. This is due to the use of the Galerkin generating system and the computation of L 2orthogonal complements. Altogether, we thus obtain a method that is only linear in the number of unknowns of the respective generalized sparse grid discretization. We report on numerical experiments for option pricing with the Kou model in one, two and three dimensions, which demonstrate the optimal complexity of our approach.