Integrating LSTM Networks with Neural Levy Processes for Financial Forecasting

Paper: arXiv 2512.07860

Authors: Mohammed Alruqimi, Luca Di Persio

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic calculus including Lévy processes, jump-diffusion SDEs, and fractional Brownian motion, while demonstrating empirical rigor through backtesting on three real-world datasets with multiple performance metrics and hyperparameter tuning.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Optimal DL-Financial Model Integration"] --> B["Input Data:<br>Brent Oil, STOXX 600, IT40 Indices"]
  B --> C["Framework Development:<br>LSTM + Merton-Lévy Jump-Diffusion"]
  C --> D["Hybrid Optimization"]
  D --> E["Performance Evaluation<br>MSE, MAE, MSPE, R²"]
  
  subgraph D ["Hybrid Optimization"]
      D1["LSTM Tuning:<br>Grey Wolf Optimizer GWO"]
      D2["Model Calibration:<br>ANN, MPA, TorchSDE"]
  end
  
  D --> F["Key Finding:<br>GWO-LSTM + ANN Calibration<br>outperforms benchmarks"]

Cited References (25)

1. Option pricing when underlying stock returns are discontinuous (1976) — link
2. Multistep Brent oil price forecasting with a multi-aspect meta-heuristic optimization and ensemble deep learning model (2024)
3. Analysis of Financial Time Series (2010) — link
4. Investment under uncertainty (2012)
5. Valuation of Commodity Futures and Options Under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot (1998)
6. The Pricing of Options and Corporate Liabilities (1973) — link
7. Empirical analysis of crude oil dynamics using affine vs. non-affine jump-diffusion models (2024) — link
8. The jump-risk premia implicit in options: evidence from an integrated time-series study (2002) — link

0 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.