# Integrating LSTM Networks with Neural Levy Processes for Financial Forecasting

arXiv: https://arxiv.org/abs/2512.07860 · HTML: https://mlsanity.com/paper/2512.07860/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Scalable Gradients for Stochastic Differential Equations](https://mlsanity.com/paper/2001.01328/) (2020)
- [A neural network-based framework for financial model calibration](https://mlsanity.com/paper/1904.10523/) (2019)
- [Jump Diffusion-Informed Neural Networks with Transfer Learning for Accurate American Option Pricing under Data Scarcity](https://mlsanity.com/paper/2409.18168/) (2024)
- [Deep Calibration With Artificial Neural Network: A Performance Comparison on Option Pricing Models](https://mlsanity.com/paper/2303.08760/) (2023)
- [Enhancing Multi-Step Brent Oil Price Forecasting with Ensemble Multi-Scenario Bi-GRU Networks](https://mlsanity.com/paper/2407.11267/) (2024)
- [Multistep Brent Oil Price Forecasting with a Multi-Aspect Meta-heuristic Optimization and Ensemble Deep Learning Model](https://mlsanity.com/paper/2407.12062/) (2024)

## Abstract (arXiv)

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-L'evy 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.