3D Tensor-based Deep Learning Models for Predicting Option Price
3D Tensor-based Deep Learning Models for Predicting Option Price
This paper addresses option pricing by introducing a 3D tensor-based data framework that integrates three information sources: fundamental data (e.g., spot price, strike price), price data (e.g., previous settle price), and Greeks (e.g., Delta, Gamma). The data is organized as a 3D tensor with three channels, each containing a 2D matrix of options versus features over time. Two deep learning models are proposed: a CNN+RNN model that uses 1D convolutions for spatial feature extraction followed by GRU layers for temporal modeling, and a Conv-LSTM model that adapts the standard convolutional LSTM by replacing 2D convolutions with 1D convolutions to match the tensor shape. Experiments on Chinese 50ETF option data from April 2018 to June 2020 show that both models outperform the Black-Scholes formula and a standard LSTM in terms of MSE, RMSE, and MAP. The Conv-LSTM with three channels achieves the best performance (MSE=0.00019, RMSE=0.01396), demonstrating the effectiveness of the tensor representation and the modified Conv-LSTM architecture. However, the Black-Scholes model yields lower MAPE, suggesting room for improvement in deep learning models for low-price scenarios. The study highlights the potential of tensor-based deep learning for financial time series prediction.
Highlights
- 1Proposes a 3D tensor-based data representation for option market information from three sources: fundamental data, price data, and Greeks.
- 2Develops two deep learning models (CNN+RNN and Conv-LSTM) tailored for 3D tensor inputs to predict option prices.
- 3Demonstrates superior performance over Black-Scholes and standard LSTM on Chinese 50ETF option data, with Conv-LSTM (3 channels) achieving the lowest MSE (0.00019) and RMSE (0.01396).
- 4Introduces a modified Conv-LSTM using 1D convolution to adapt to the option data's tensor shape, preserving cross-channel correlations.
Methods
- M3D tensor representation: organizes option data into three channels (fundamental, price, Greeks) as 2D matrices (options × features) over time.
- MCNN+RNN model: uses 1D convolutional layers for spatial feature extraction followed by GRU layers for temporal modeling, with a final regression module.
- MConv-LSTM model: replaces 2D convolutions in standard Conv-LSTM with 1D convolutions to handle the (T, C, N, D) tensor shape, capturing both spatial and temporal dependencies.
Results
- RConv-LSTM with 3 channels outperforms all models: MSE=0.00019, RMSE=0.01396, MAP=0.00848, PCC=0.96941.
- RCNN+RNN achieves MSE=0.00025, RMSE=0.01585, MAP=0.01227, PCC=0.95609, better than LSTM and B-S.
- RB-S model has the lowest MAPE (0.47957) but higher MSE (0.00082) and RMSE (0.02872), indicating poor performance at low prices.
- RAll deep learning models show strong linear correlation with true prices (PCC > 0.95).
- RConv-LSTM with 1 channel (MSE=0.00028) underperforms the 3-channel version, validating the multi-source tensor representation.
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