Mean-Variance Portfolio Optimization with Nonlinear Derivative Securities.

In this paper, we propose a simulation approach to mean-variance optimization for portfolios comprised of derivative securities. The key of the proposed method is on the development of an unbiased and consistent estimator of the covariance matrix of asset returns which do not admit closed-form formulas but require Monte Carlo estimation, leading to a sample-based optimization problem that is easy to solve. We characterize the asymptotic properties of the proposed covariance estimator, and the solution to and the objective value of the sample-based optimization problem. Performance of the proposed approach is demonstrated via numerical experiments.