Adaptive numerical integration and control variates for pricing Basket   Options
  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. 
Christophe De Luigi (LSIS), J\'er\^ome Lelong (LJK), Sylvain Maire   (LSIS)
math.PR math.NA