An application of an n-dimensional fuzzy smoothing filter in financial modeling

Data smoothing is an important step within a data processing procedure that allows one to stress the most important pattern of a function relation between a studied object and given variables. Recently, Holčapek and Tichý (2011) suggested a smoothing filter based on fuzzy transform approach of Perfilieva (2004) and compared it to Nadaraya-Watson estimator. However, within the analysis only one independent variable was assumed. By contrast, many real world problems are multidimensional and hence in this paper we generalize the fuzzy smoothing filter into two dimensions and show its application within a common problem of financial engineering and asset pricing, the option implied volatility surface presentation.