Bounding Option Prices by Semidefinite Programming: A Cutting Plane Algorithm

In a recent article, Bertsimas and Popescu showed that a tight upper bound on a Europeantype call option price, given the first n moments of the distribution of the underlying security price, can be obtained by solving an associated semidefinite programming problem (SDP). The purpose of this paper is to improve and extend their results. We will show that a tight lower bound can be calculated by solving another SDP. Also, we will show that these problems can be solved very quickly by a newly developed cutting plane algorithm when n is less than six or seven.