SC²S Colloquium - October, 16, 2008
|Time:||4:30 pm, s.t.|
16:30 Uhr - Deepak Pandey: Regression with Spatially Adaptive Sparse Grids in Financial Applications (MA)
The aim of Regression is to identify and model dependencies between a dependent variable and one or multiple independent variables in numerical data. Regression techniques compute a "best fit" to the data with regard to some metrik. Mostly, least squares or related measures are used to determine the quality of the fit. Given a function space, the function that best fits the data is to be identified.
Spatially adaptive sparse grids shall be examined for the estimation of "best fit" functions with respect to the least square measure. This is needed in financial applications, for example in path dependent options, such as the American option. Especially non-smoothness and extrapolation into areas with few points have to be dealt with.
In this thesis, new kinds of basis functions for sparse grids have been examined and introduced for regularization. Evaluation has been done for artificial analytical functions as well as for real-world options (Bermudean, Spread and Basket Options). The sparse grid package has been extended and included in the Thetaris Software.