SC²S Colloquium - April 07, 2011
|Date:||April 7, 2011|
|Time:||15:00 pm, s.t.|
Sarpkan Selçuk: Non-Equidistant Sparse Grids for a PDE Solver in Computational Finance (MA)
The topic of this master thesis is the implementation of a grid stretching into the currently existing sparse grid Black-Scholes solver of the SGpp code of our chair. A means of grid stretching is appended to the already implemented solver for the sparse grids with equidistant points in the same hierarchy. Grid Stretching can be analytic or discrete. The analytic case refers to a stretching function used to stretch the grid. In the discrete case, the grid is generated via a sample of the grid points provided. The rest of the grid points due to the hierarchically lower levels are then an interpolation of the given points. We compare the numerical and performance results of the original solver with that of the solver which applies stretching. The results are promising. In order to get the same accuracy one needs less levels in many cases, the implemented stretching class also does not give much of an overhead compared to the original non-stretched solver.