Parallel architecture of CNN‐bidirectional LSTMs for implied volatility forecast

We propose a new forecast method based on artificial neural networks (ANNs), ensemble CNN‐BiLSTM, which is an ensemble of three CNN‐BiLSTMs constructed with the combination of Convolution Neural Network (CNN) and Bidirectional Long Short‐Term Memory (BiLSTM). The new forecast method effectively handles the strong long memory serial dependence feature of the daily VXN by the ensemble CNN‐BiLSTM together with proper normalization and batch size. The long memory features arising from time‐dependent mean and variance are largely reduced by normalizing the data with local mean and local standard deviation (SD). The batch size is determined by the optimal block length of the moving block bootstrap which reflects the long memory. The ensemble CNN‐BiLSTM concentrates on 1‐day, 1‐week, and 2‐week features of the normalized VXN data. An out‐of‐sample forecast comparison reveals that (i) the proposed ensemble CNN‐BiLSTM has better forecast performance than the autoregressive model, DNN, LSTM, BiLSTM, and individual CNN‐BiLSTMs; (ii) the local mean‐SD normalization has superior forecast performance to the standard global mean‐SD normalization; (iii) and the optimal block length improves the forecast performance over a batch size considered in the literature.