Volatility is a key variable in option pricing, trading and hedging strategies. The purpose of this paper is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training-subset selection methods. These methods manipulate the training data in order to improve the out of sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models which are not adapted to some out of sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training-subset selection methods are proposed based on random, sequential or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases errors. Using real data from SP500 index options, these techniques are compared to the static subset selection method. Based on MSE total and percentage of non fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, specially those obtained from the adaptive random training subset selection method applied to the whole set of training samples.

中文翻译：

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使用遗传编程的动态训练子集选择方法预测隐含波动率

波动率是期权定价、交易和对冲策略的关键变量。本文的目的是通过动态训练子集选择方法使用遗传规划 (GP) 的扩展来提高预测隐含波动率的准确性。这些方法操纵训练数据以改进样本外模式拟合。当与使用单个训练数据样本的静态子集选择方法一起应用时，GP 可以生成不适应某些样本外健康情况的预测模型。为了提高生成的 GP 模式的预测精度，在 GP 算法中引入了动态子集选择方法，允许在进化过程中定期更改训练样本。提出了四种基于随机的动态训练子集选择方法，顺序或自适应子集选择。最新的方法使用自适应子集权重，根据适应度案例误差测量样本难度。使用来自 SP500 索引选项的真实数据，将这些技术与静态子集选择方法进行比较。基于 MSE 总数和非拟合观测值的百分比，结果表明，动态方法提高了生成的 GP 模型的预测性能，特别是那些从应用于整个训练样本集的自适应随机训练子集选择方法中获得的模型。