Previous research on option strategies has primarily focused on their behavior near expiration, with limited attention to the transient value process of the portfolio. In this paper, we formulate Iron Condor portfolio optimization as a stochastic optimal control problem, examining the impact of the control process \( u(k_i, τ) \) on the portfolio's potential profitability and risk. By assuming the underlying price process as a bounded martingale within $[K_1, K_2]$, we prove that the portfolio with a strike structure of $k_1 < k_2 = K_2 < S_t < k_3 = K_3 < k_4$ has a submartingale value process, which results in the optimal stopping time aligning with the expiration date $τ= T$. Moreover, we construct a data generator based on the Rough Heston model to investigate general scenarios through simulation. The results show that asymmetric, left-biased Iron Condor portfolios with $τ= T$ are optimal in SPX markets, balancing profitability and risk management. Deep out-of-the-money strategies improve profitability and success rates at the cost of introducing extreme losses, which can be alleviated by using an optimal stopping strategy. Except for the left-biased portfolios $τ$ generally falls within the range of [50\%,75\%] of total duration. In addition, we validate these findings through case studies on the actual SPX market, covering bullish, sideways, and bearish market conditions.
On the Profitability of Optimal Mean Reversion Trading Strategies
本文研究了美国股票市场最优均值回归交易策略的盈利能力。与常规的配对交易不同，本文采用极大似然法构造了最符合Ornstein-Uhlenbeck过程的最优静态配对交易组合，并对模型参数进行了严格估计。因此，我们在交易前确保我们的投资组合符合均值回归过程。然后，我们使用模型参数生成反向交易信号。并通过多次检验对阈值和样本内期长度进行了优化。在九个好的配对例子中，我们可以看到我们的配对在样本内和样本外的时间段内都表现出很高的夏普比率（超过1.9）。特别地，Crown Castle International Corp.（CCI）和HCP，Inc. (HCP)在样本内测试期间，达到夏普比率2.326，在样本外测试期间，达到夏普比率2.425。皇冠城堡国际公司（CCI）和房地产收入公司（O）在样本内和样本外期间分别达到2.405和2.903的夏普比率。
