An ADI Sparse Grid method for Pricing Efficiently American Options under the Heston Model

One goal of financial research is to determine fair prices on the financial market. As financial models and the data sets on which they are based are becoming ever larger and thus more complex, financial instruments must be further developed to adapt to the new complexity, with short runtimes and efficient use of memory space. Here we show the effects of combining known strategies and incorporating new ideas to further improve numerical techniques in computational finance. In this paper we combine an ADI (alternating direction implicit) scheme for the temporal discretization with a sparse grid approach and the combination technique. The later approach considerably reduces the number of "spatial" grid points. The presented standard financial problem for the valuation of American options using the Heston model is chosen to illustrate the advantages of our approach, since it can easily be adapted to other more complex models.