Paper: arXiv 2403.00746

Abstract

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial differential equation is reformulated as an energy minimization problem, which is approximated in a time-stepping fashion by deep artificial neural networks. The proposed scheme respects the asymptotic behavior of option prices for large levels of moneyness, and adheres to a priori known bounds for option prices. The accuracy and efficiency of the proposed method is assessed in a series of numerical examples, with particular focus in the lifted Heston model.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel deep learning method for solving high-dimensional PDEs derived from rough volatility models, requiring advanced mathematics in gradient flows and neural network optimization. It includes numerical experiments (e.g., lifted Heston model) with error metrics and computational details, but lacks extensive real-world backtesting or code/data, placing it in the high-math, high-rigor quadrant.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Develop efficient pricing method for<br>European options in high-dimensional<br>rough diffusion models"] --> B["Methodology: Reformulate PDE as<br>Energy Minimization Problem"]
  B --> C["Time-stepping Approximation:<br>Deep Neural Networks"]
  C --> D["Computational Process:<br>Approximate value function via<br>sequential network training"]
  D --> E["Data/Inputs:<br>Lifted Heston Model &<br>Diffusion Models"]
  E --> F["Outcomes:<br>1. Asymptotic behavior respected<br>2. A priori bounds adhered to<br>3. Accurate & Efficient<br>4. High-dimensional capability"]