Differential Evolution Optimization of the Broken Wing Butterfly Option Strategy

Abstract

The Broken Wing Butterfly (BWB) has become a popular options strategy for traders. Profit is generated primarily by exploiting option value time decay. In this paper the selection of the option strikes to be used along with trade entry and exit parameters, such as time to expiration and profit and loss targets, are optimized using over a decade of historical option data of the S & P 500 exchange traded fund (symbol: SPY). The importance of selecting an optimal strike mapping method, by which strikes are assigned in any time period, is highlighted. Of the three methods considered, the normalized strike mapping method was found to be optimal. Optimization was performed using a differential evolution (DE) evolutionary algorithm. The objective function used for optimization considered final cumulative profit, volatility, and maximum equity drawdown while achieving a high trade win rate. A trade example is given to illustrate the use of the obtained results.