Minimizing Effective Dimension using Linear Transformation

In recent years, constructions based on Brownian bridge [11], principal component analysis[1], and linear transformation [7] have been proposed in the context of derivative pricing to further enhance QMC through dimension reduction. Motivated by [16, 18] and the ANOVA decomposition, this paper (i) formally justifies the dimension minimizing algorithm of Tan and Imai [7], and (ii) proposes a new formulation of linear transformation which explicitly reduces the effective dimension (in the truncation sense) of a function. Another new application of LT method to an interest rate model is considered. We establish the situation for which linear transformation method outperforms PCA. This method is not only effective on dimension reduction, it is also robust and can easily be extended to general diffusion processes.