Basket problems in margin calculation: Modelling and algorithms

This paper considers combinatorial models and algorithms for the problems of constructing a basket of stock positions representing a capitalization-weighted market index for the purpose to be offset in the margin calculation by a position in other index products as index options, futures or participation units. We show how following the regulatory definition of the basket a 0–1 programming model of knapsack type can be obtained and how to develop the related efficient exact or approximation grab-the-basket algorithms. All approximations are supplied by the performance guarantee evaluations.