Parallel investments in multiple call and put options for the tracking of desired profit profiles

A hierarchical algorithm is presented for optimally and automatically combining various option investments to cost-efficiently realize a desired profit-vs.-underlying-price profile (profit profile). The algorithm assumes that a user-defined reference shape is defined and a set of plain vanilla options in which long and short investment positions can be taken are given. Within the presented framework, the desired profit profile can be of arbitrary piecewise-affine (PWA) shape. Depending on future underlying price predictions, it typically represents a bearish or bullish market outlook, or displays bi-modal shape for conditional market outlooks. The method provides a tool for portfolio optimization that is flexible enough to trade off different user-preferences such as exploiting on conditional market outlooks, realizing leverage, and most notably guaranteeing predictable worst-case losses for risk-minimization. The framework can easily be extended to account for different derivative contracts such as exotic options.