The purpose of this paper is to improve the accuracy of dynamic hedging using implied volatilities generated by genetic programming. Using real data from S&P500 index options, the genetic programming's ability to forecast Black and Scholes implied volatility is compared between static and dynamic training-subset selection methods. The performance of the best generated GP implied volatilities is tested in dynamic hedging and compared with Black-Scholes model. Based on MSE total, the dynamic training of GP yields better results than those obtained from static training with fixed samples. According to hedging errors, the GP model is more accurate almost in all hedging strategies than the BS model, particularly for in-the-money call options and at-the-money put options.

中文翻译：

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使用生成的遗传编程隐含波动率模型进行动态对冲

本文的目的是利用遗传编程产生的隐含波动率来提高动态对冲的准确性。使用来自标准普尔 500 指数期权的真实数据，在静态和动态训练子集选择方法之间比较了遗传编程预测 Black 和 Scholes 隐含波动率的能力。在动态对冲中测试了最佳生成的 GP 隐含波动率的性能，并与 Black-Scholes 模型进行了比较。基于 MSE 总量，GP 的动态训练比固定样本的静态训练产生更好的结果。根据套期保值误差，GP 模型几乎在所有套期保值策略中都比 BS 模型更准确，尤其是价内看涨期权和价内看跌期权。