This paper shows a novel machine learning model for realized volatility (RV) prediction using a normalizing flow, an invertible neural network. Since RV is known to be skewed and have a fat tail, previous methods transform RV into values that follow a latent distribution with an explicit shape and then apply a prediction model. However, knowing that shape is non-trivial, and the transformation result influences the prediction model. This paper proposes to jointly train the transformation and the prediction model. The training process follows a maximum-likelihood objective function that is derived from the assumption that the prediction residuals on the transformed RV time series are homogeneously Gaussian. The objective function is further approximated using an expectation-maximum algorithm. On a dataset of 100 stocks, our method significantly outperforms other methods using analytical or naive neural-network transformations.

翻译：本文提出了一种利用归一化流（可逆神经网络）进行实现波动率预测的新型机器学习模型。由于实现波动率具有偏态和厚尾特性，以往方法通常先将其转换为服从特定显式形状潜在分布的数值，再应用预测模型。然而，准确确定分布形状并非易事，且转换结果直接影响预测模型性能。本文提出对转换过程与预测模型进行联合训练。该训练过程遵循基于转换后实现波动率时间序列预测残差服从齐次高斯假设而推导的最大似然目标函数，并通过期望最大化算法对该目标函数进行近似。在包含100只股票的数据集上，我们的方法显著优于使用解析方法或朴素神经网络转换的其他方法。