Bounding Option Prices of Multi-Assets: A Semidefinite Programming Approach

Recently, semidefinite programming has been used to bound the price of a single-asset European call option at a fixed time. Given the first n moments, a tight bound can be obtained by solving a single semidefinite programming problem of dimension n + 1. In this paper, we study the multi-asset case, which is generally more practical than the single-asset case. We construct a sequence of semidefinite programming relaxations. As the dimension of the semidefinite relaxations increases, the bound becomes more accurate and converges to the tight bound. Some numerical results are reported to illustrate the method.