Integrating LSTM Networks with Neural Levy Processes for Financial Forecasting

TL;DR

The paper addresses asset price forecasting by fusing LSTM networks with stochastic jump-diffusion models, specifically Lévy–Merton Jump-Diffusion and Fractional Heston. It introduces three calibration approaches—neural networks, TorchSDE, and Marine Predators Algorithm—and uses Grey Wolf Optimizer to tune LSTM hyperparameters. Empirical results on Brent oil, STOXX 600, and IT40 show that NN-calibrated Lévy–Merton with GWO-tuned LSTM provides the best accuracy and robustness among the tested configurations. The work demonstrates the value of integrating neural calibration with continuous-time stochastic models for improved forecasting and highlights directions for more sophisticated jump structures and regularization techniques.

Abstract

This paper investigates an optimal integration of deep learning with financial models for robust asset price forecasting. Specifically, we developed a hybrid framework combining a Long Short-Term Memory (LSTM) network with the Merton-Lévy jump-diffusion model. To optimise this framework, we employed the Grey Wolf Optimizer (GWO) for the LSTM hyperparameter tuning, and we explored three calibration methods for the Merton-Levy model parameters: Artificial Neural Networks (ANNs), the Marine Predators Algorithm (MPA), and the PyTorch-based TorchSDE library. To evaluate the predictive performance of our hybrid model, we compared it against several benchmark models, including a standard LSTM and an LSTM combined with the Fractional Heston model. This evaluation used three real-world financial datasets: Brent oil prices, the STOXX 600 index, and the IT40 index. Performance was assessed using standard metrics, including Mean Squared Error (MSE), Mean Absolute Error(MAE), Mean Squared Percentage Error (MSPE), and the coefficient of determination (R2). Our experimental results demonstrate that the hybrid model, combining a GWO-optimized LSTM network with the Levy-Merton Jump-Diffusion model calibrated using an ANN, outperformed the base LSTM model and all other models developed in this study.

Figures (6)

• Figure 1: The proposed framework
• Figure 2: Left: Normal compound Poisson process simulation. $\lambda$ = 10, T = 1y, jumps $\sim$ N(0, 0.22). 10 jumps per year on average, the magnitude of the jumps follows a normal distribution N(0, 0.22). Right: Merton jump diffusion process simulation. $S_0$ = 100, $\mu$ = $5\%$, $\sigma$ = 20$\%$, $\lambda = 10, T = 5y$, jumps $\sim N(0, 0.12), \delta t = 5 / 1000$.
• Figure 3: LSTM-Lévy model performance on the Brent Dataset. The figures, arranged from top-left, present the results obtained using the three calibration methods: NN-based calibration, MPA-based calibration, and TorchSDE-based calibration of the Merton model, along with the performance of a standalone LSTM model.
• Figure 4: LSTM-Lévy model performance on the STOXX 600 Dataset. The figures, arranged from top-left, present the results obtained using the three calibration methods: NN-based calibration, MPA-based calibration, and TorchSDE-based calibration of the Merton model, along with the performance of a standalone LSTM model.
• Figure 5: LSTM-Lévy model performance on the IT40 Dataset. The figures, arranged from top-left, present the results obtained using the three calibration methods: NN-based calibration, MPA-based calibration, and TorchSDE-based calibration of the Merton model, along with the performance of a standalone LSTM model.