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A hybrid wavelet-based physics-informed neural network for portfolio management

Bahadur Yadav, Mahaprasad Mohanty, Ratikanta Behera, Sanjay Kumar Mohanty

Abstract

In this paper, we present a Hybrid Wavelet-based Physics-Informed Neural Networks (HW-PINNs) framework for portfolio management that provides a promising alternative to Physics-Informed Neural Networks (PINNs). Here, we first discuss the generalized framework of the Merton jump diffusion model and the associated HW-PINNs, followed by the one-dimensional case of a European option. Our work adapts the HW-PINN framework to the Merton jump-diffusion model for a European option, using a simplified direct coefficient optimization strategy, a mathematically corrected log-space formulation, and an efficient FFT -based computation of the integro-differential operator. Through numerical experiments across realistic market scenarios, we show that our proposed model achieves high accuracy and robustness, with a mean relative error of 0.27\% in low jump intensity scenarios compared to high-fidelity benchmarks. Our results validate that the implementation of this specific HW-PINN framework is a computationally efficient and reliable tool for pricing derivatives in markets with high jump risk. In addition, we further discuss risk analysis using Value at Risk (VaR) and Conditional Value at Risk (CVaR), which provide insights into downside risk across different market scenarios.

A hybrid wavelet-based physics-informed neural network for portfolio management

Abstract

In this paper, we present a Hybrid Wavelet-based Physics-Informed Neural Networks (HW-PINNs) framework for portfolio management that provides a promising alternative to Physics-Informed Neural Networks (PINNs). Here, we first discuss the generalized framework of the Merton jump diffusion model and the associated HW-PINNs, followed by the one-dimensional case of a European option. Our work adapts the HW-PINN framework to the Merton jump-diffusion model for a European option, using a simplified direct coefficient optimization strategy, a mathematically corrected log-space formulation, and an efficient FFT -based computation of the integro-differential operator. Through numerical experiments across realistic market scenarios, we show that our proposed model achieves high accuracy and robustness, with a mean relative error of 0.27\% in low jump intensity scenarios compared to high-fidelity benchmarks. Our results validate that the implementation of this specific HW-PINN framework is a computationally efficient and reliable tool for pricing derivatives in markets with high jump risk. In addition, we further discuss risk analysis using Value at Risk (VaR) and Conditional Value at Risk (CVaR), which provide insights into downside risk across different market scenarios.
Paper Structure (11 sections, 33 equations, 10 figures, 2 tables, 1 algorithm)

This paper contains 11 sections, 33 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Portfolio Optimization under Jump Risk
  3. European Option in the Merton Jump Diffusion Model
  4. Hybrid Wavelet-based Physics-Informed Neural Networks
  5. Training Architecture and Loss Function
  6. Training Data Generation
  7. Experimental Result and Discussion
  8. Model Performance across Several Market Scenarios
  9. Low Jump Intensity Case
  10. Risk Analysis Using Value at Risk and Conditional Value at Risk
  11. Conclusion

Figures (10)

  • Figure 1: Architecture diagram of our proposed approach.
  • Figure 2: Distribution of the 8,192 training points (blue), initial condition points (red), and boundary condition points (green) across the price-time domain.
  • Figure 3: HW-PINN learns the option price surface.
  • Figure 4: Training characteristics in the low jump intensity scenario.
  • Figure 5: Comparison of PINN and HW-PINN with benchmark solution.
  • ...and 5 more figures