Adaptive numerical integration and control variates for pricing Basket Options
For practitioners pricing multidimensional options, this method offers improved accuracy and efficiency, though it is an incremental improvement over existing adaptive integration techniques.
The paper develops a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework, improving adaptive integration with a new splitting strategy and using it as a control variate after PCA-based dimension reduction. Numerical tests show effectiveness for basket, put on minimum, and digital options up to dimension ten.
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting strategy based on a geometrical criterion. In higher dimensions, this new algorithm is used as a control variate after a dimension reduction based on principal component analysis. Numerical tests are performed on the pricing of basket, put on minimum and digital options in dimensions up to ten.