Constrained deep learning for pricing and hedging european options in incomplete markets

• URL: http://arxiv.org/abs/2511.20837v1
• Date: Tue, 25 Nov 2025 20:40:01 GMT
• Title: Constrained deep learning for pricing and hedging european options in incomplete markets
• Authors: Nicolas Baradel,
• Abstract summary: In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks.<n>This paper introduces a constrained deep learning approach to determine option prices and hedging strategies that minimize the Profit and Loss distribution around zero.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In incomplete financial markets, pricing and hedging European options lack a unique no-arbitrage solution due to unhedgeable risks. This paper introduces a constrained deep learning approach 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 enforcing the self-financing portfolio condition. A key challenge arises from the non-smooth nature of option payoffs (e.g., vanilla calls are non-differentiable at-the-money, while digital options are discontinuous), which conflicts with the inherent smoothness of standard neural networks. To address this, we compare unconstrained networks against constrained architectures that explicitly embed the terminal payoff condition, drawing inspiration from PDE-solving techniques. Our framework assumes two tradable assets: the underlying and a liquid call option capturing volatility dynamics. Numerical experiments evaluate the method on simple options with varying non-smoothness, the exotic Equinox option, and scenarios with market jumps for robustness. Results demonstrate superior P&L distributions, highlighting the efficacy of constrained networks in handling realistic payoffs. This work advances machine learning applications in quantitative finance by integrating boundary constraints, offering a practical tool for pricing and hedging in incomplete markets.

Related papers

• Robust Reinforcement Learning in Finance: Modeling Market Impact with Elliptic Uncertainty Sets [57.179679246370114]
  In financial applications, reinforcement learning (RL) agents are commonly trained on historical data, where their actions do not influence prices.<n>During deployment, these agents trade in live markets where their own transactions can shift asset prices, a phenomenon known as market impact.<n>Traditional robust RL approaches address this model misspecification by optimizing the worst-case performance over a set of uncertainties.<n>We develop a novel class of elliptic uncertainty sets, enabling efficient and tractable robust policy evaluation.
  arXiv  Detail & Related papers  (2025-10-22T18:22:25Z)
• FinTSB: A Comprehensive and Practical Benchmark for Financial Time Series Forecasting [58.70072722290475]
  Financial time series (FinTS) record the behavior of human-brain-augmented decision-making.<n>FinTSB is a comprehensive and practical benchmark for financial time series forecasting.
  arXiv  Detail & Related papers  (2025-02-26T05:19:16Z)
• The AI Black-Scholes: Finance-Informed Neural Network [11.339331636751329]
  In option pricing, existing models are typically classified into principle-driven methods and data-driven approaches.<n>In contrast, data-driven models excel in capturing market data trends, but they often lack alignment with core financial principles.<n>This work proposes a hybrid approach to address these limitations by integrating the strengths of both principled and data-driven methodologies.
  arXiv  Detail & Related papers  (2024-12-15T22:40:40Z)
• A Tale of Two Cities: Pessimism and Opportunism in Offline Dynamic Pricing [20.06425698412548]
  This paper studies offline dynamic pricing without data coverage assumption. We establish a partial identification bound for the demand parameter whose associated price is unobserved. We incorporate pessimistic and opportunistic strategies within the proposed partial identification framework to derive the estimated policy.
  arXiv  Detail & Related papers  (2024-11-12T19:09:41Z)
• Diffusion Variational Autoencoder for Tackling Stochasticity in Multi-Step Regression Stock Price Prediction [54.21695754082441]
  Multi-step stock price prediction over a long-term horizon is crucial for forecasting its volatility. Current solutions to multi-step stock price prediction are mostly designed for single-step, classification-based predictions. We combine a deep hierarchical variational-autoencoder (VAE) and diffusion probabilistic techniques to do seq2seq stock prediction. Our model is shown to outperform state-of-the-art solutions in terms of its prediction accuracy and variance.
  arXiv  Detail & Related papers  (2023-08-18T16:21:15Z)
• Online Learning under Budget and ROI Constraints via Weak Adaptivity [57.097119428915796]
  Existing primal-dual algorithms for constrained online learning problems rely on two fundamental assumptions. We show how such assumptions can be circumvented by endowing standard primal-dual templates with weakly adaptive regret minimizers. We prove the first best-of-both-worlds no-regret guarantees which hold in absence of the two aforementioned assumptions.
  arXiv  Detail & Related papers  (2023-02-02T16:30:33Z)
• Beyond Surrogate Modeling: Learning the Local Volatility Via Shape Constraints [0.0]
  We explore the abilities of two machine learning approaches for no-arbitrage of European vanilla option prices, which jointly yield the corresponding local volatility surface. We demonstrate the performance of these approaches relative to the SSVI industry standard. The GP approach is proven arbitrage-free, whereas arbitrages are only penalized under the SSVI and NN approaches.
  arXiv  Detail & Related papers  (2022-12-20T02:17:47Z)
• A Unifying Framework for Online Optimization with Long-Term Constraints [62.35194099438855]
  We study online learning problems in which a decision maker has to take a sequence of decisions subject to $m$ long-term constraints. The goal is to maximize their total reward, while at the same time achieving small cumulative violation across the $T$ rounds. We present the first best-of-both-world type algorithm for this general class problems, with no-regret guarantees both in the case in which rewards and constraints are selected according to an unknown model, and in the case in which they are selected at each round by an adversary.
  arXiv  Detail & Related papers  (2022-09-15T16:59:19Z)
• Online Learning with Knapsacks: the Best of Both Worlds [54.28273783164608]
  We casting online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$m resource constraints. Our framework allows the decision maker to handle its evidence flexibility and costoretic functions.
  arXiv  Detail & Related papers  (2022-02-28T12:10:48Z)
• Arbitrage-free neural-SDE market models [6.145654286950278]
  We develop a nonparametric model for the European options book respecting underlying financial constraints. We study the inference problem where a model is learnt from discrete time series data of stock and option prices. We use neural networks as function approximators for the drift and diffusion of the modelled SDE system.
  arXiv  Detail & Related papers  (2021-05-24T00:53:10Z)
• Deep Hedging: Learning Risk-Neutral Implied Volatility Dynamics [0.0]
  numerically efficient approach for learning a risk-neutral measure for paths of simulated spot and option prices. We show that market dynamics are free from "statistical arbitrage" in the absence of transaction costs if and only if they follow a risk-neutral measure.
  arXiv  Detail & Related papers  (2021-03-22T15:38:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.