%0 Journal Article %T Optimal Static Quadratic Hedging %A Tim Leung %A Matthew Lorig %J Quantitative Finance %D 2015 %I arXiv %X We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these expectations analytically in a general Markov diffusion market. To illustrate the versatility of our approach, we present several numerical examples, including hedging path-dependent options and options written on a correlated asset. %U http://arxiv.org/abs/1506.02074v2