Option overlay strategies

Option overlays on a rebalanced portfolio are designed. Inputs to the design problem are the physical and risk neutral probabilities at the option maturity. They are estimated from time series and option data, respectively. The objective for the design is the bid price of a two price economy modelled as a distorted expectation. The design is monotone increasing in the underlier with a delta constraint. The option positioning is implemented on the S&P 500 index, supposedly rebalanced every 21 days with option positions taken 10 days prior to a rebalance date with a maturity near two months. Option overlays are seen to raise performance measures and reduce drawdowns.