Finance-Insurance
Time: 15.00 am
Date:19th of January 2025
Room 3049

Nicolas BARADEL (Inria) “Constrained deep learning for pricing and hedging European options: towards reinforcement learning extensions.”

Abstract : In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. We introduce a constrained deep learning framework to determine option prices and hedging strategies that minimize the Profit and Loss (P&L) distribution around zero. We employ a single neural network to represent the option price function, with its gradient serving as the hedging strategy, optimized via a loss function that enforces the self-financing portfolio condition. A major difficulty stems from the non-smooth nature of option payoffs (e.g., vanilla calls are non-differentiable at-the-money, digital options are discontinuous), which conflicts with the intrinsic smoothness of standard neural networks. To overcome this, we compare unconstrained architectures with constrained networks that explicitly incorporate the terminal payoff condition, drawing inspiration from PDE boundary embedding techniques. We further explore an extension of this framework by integrating Howard’s policy iteration algorithm within a reinforcement learning perspective. This direction aims to leverage the efficiency of policy iteration while preserving the terminal payoff constraint through the constrained network architecture.

Organizers:  Jean-David FERMANIAN