Tracking Error Analysis of Optioned Portfolio Optimization

In this paper, a target tracking problem for the portfolio selection involving options is studied. In particular, the portfolio in question contains a stock index and some European style options on the index. And the tracking models with fixed or random target values are investigated, respectively. The tracking-error-variance (TEV) methodology is adopted in our approach to formulate the problems, and the optimal solutions are derived based on optimality conditions. Attention is paid to the structures of the optimal payoffs in both cases, which are shown to possess rich properties. Throughout the paper, numerical examples are presented to illustrate and validate our results.