Option pricing bounds via semidefinite programming

This paper develops optimization based bounds on option prices by using a sub or super replicating portfolio of assets whose value at discrete time points can be expressed as piecewise polynomial functions. The optimization problems are polynomial programs which we modify and solve by the sum-of-squares methodology. A dual formulation is then developed, which formulates bounds in terms of an optimization problem involving moment matrices of measures consistent with the prices of tradable assets. The bounds are examined using the standard. Black-Scholes option pricing model.