We present a two-stage stochastic program with recourse to construct covered call portfolios. To maximize the expected utility of a covered call portfolio, the model selects equity positions and call option overwriting weights for varying strike prices and expiry dates. Since the model has linear constraints and risk-averse utility functions are concave, the optimization problem is convex. The model is tested using 67 U.S. large-cap equities and optimizing the quadratic, negative exponential, and power utility functions. The expected utility is modeled as the average utility of the portfolio in a number of scenarios. Scenarios are first generated randomly then moment matching is employed, allowing the model to produce high quality results with a relatively small number of scenarios. To improve solution times we use a progressive hedging decomposition.

我们提出了一个具有阶段性的两阶段随机程序，该程序可用于构造涵盖的看涨期权组合。为了最大程度地提高有担保看涨期权组合的预期效用，该模型针对不同的执行价格和到期日选择股票头寸和看涨期权覆盖权重。由于模型具有线性约束并且规避风险的效用函数是凹的，因此优化问题是凸的。该模型使用67个美国大型股票进行了测试，并优化了二次方，负指数方和幂效用函数。在许多情况下，将预期效用建模为投资组合的平均效用。首先随机生成方案，然后采用矩匹配，从而使模型能够以相对较少的方案产生高质量的结果。