In this short article, we describe how the correlation of typical diffusion processes arising e.g. in financial modelling can be exploited-by means of asymptotic analysis of principal components-to make Feynman-Kac PDEs of high dimension computationally tractable. We explore the links to dimension adaptive sparse grids (Gerstner and Griebel, Computing 71:65-87, 2003), anchored ANOVA decompositions and dimension-wise integration (Griebel and Holtz, J Complexity 26:455-489, 2010), and the embedding in infinite-dimensional weighted spaces (Sloan and Wozniakowski, J Complexity 14:1-33, 1998). The approach is shown to give sufficient accuracy for the valuation of index options in practice. These numerical findings are backed up by a complexity analysis that explains the independence of the computational effort of the dimension in relevant parameter regimes.
展开▼
