Optimal hedging for multivariate derivatives based on additive models

In this paper, we consider optimal hedges for a class of derivative securities whose underlyings are untraded, using the additive sum of smooth functions of traded assets that minimizes the mean square error. Based on the necessary and sufficient condition, we derive a methodology to compute optimal smooth functions efficiently by solving a system of linear equations. Moreover, we extend the idea to basket options consisting of a portfolio of stocks, where individual payoff functions of traded assets are optimally computed. We also provide numerical experiments to illustrate our methodology.