Options

Beta-Dependent Gamma Feedback and Endogenous Volatility Amplification in Option Markets ArXiv ID: 2511.22766 “View on arXiv” Authors: Haoying Dai Abstract We develop a theoretical framework that aims to link micro-level option hedging and stock-specific factor exposure with macro-level market turbulence and explain endogenous volatility amplification during gamma-squeeze events. By explicitly modeling market-maker delta-neutral hedging and incorporating beta-dependent volatility normalization, we derive a stability condition that characterizes the onset of a gamma-squeeze event. The model captures a nonlinear recursive feedback loop between market-maker hedging and price movements and the resulting self-reinforcing dynamics. From a complex-systems perspective, the dynamics represent a bounded nonlinear response in which effective gain depends jointly on beta-normalized shock perception and gamma-scaled sensitivity. Our analysis highlights that low-beta stocks exhibit disproportionately strong feedback even for modest absolute price movements. ...

Option market making with hedging-induced market impact ArXiv ID: 2511.02518 “View on arXiv” Authors: Paulin Aubert, Etienne Chevalier, Vathana Ly Vath Abstract This paper develops a model for option market making in which the hedging activity of the market maker generates price impact on the underlying asset. The option order flow is modeled by Cox processes, with intensities depending on the state of the underlying and on the market maker’s quoted prices. The resulting dynamics combine stochastic option demand with both permanent and transient impact on the underlying, leading to a coupled evolution of inventory and price. We first study market manipulation and arbitrage phenomena that may arise from the feedback between option trading and underlying impact. We then establish the well-posedness of the mixed control problem, which involves continuous quoting decisions and impulsive hedging actions. Finally, we implement a numerical method based on policy optimization to approximate optimal strategies and illustrate the interplay between option market liquidity, inventory risk, and underlying impact. ...

Risk-Sensitive Option Market Making with Arbitrage-Free eSSVI Surfaces: A Constrained RL and Stochastic Control Bridge ArXiv ID: 2510.04569 “View on arXiv” Authors: Jian’an Zhang Abstract We formulate option market making as a constrained, risk-sensitive control problem that unifies execution, hedging, and arbitrage-free implied-volatility surfaces inside a single learning loop. A fully differentiable eSSVI layer enforces static no-arbitrage conditions (butterfly and calendar) while the policy controls half-spreads, hedge intensity, and structured surface deformations (state-dependent rho-shift and psi-scale). Executions are intensity-driven and respond monotonically to spreads and relative mispricing; tail risk is shaped with a differentiable CVaR objective via the Rockafellar–Uryasev program. We provide theory for (i) grid-consistency and rates for butterfly/calendar surrogates, (ii) a primal–dual grounding of a learnable dual action acting as a state-dependent Lagrange multiplier, (iii) differentiable CVaR estimators with mixed pathwise and likelihood-ratio gradients and epi-convergence to the nonsmooth objective, (iv) an eSSVI wing-growth bound aligned with Lee’s moment constraints, and (v) policy-gradient validity under smooth surrogates. In simulation (Heston fallback; ABIDES-ready), the agent attains positive adjusted P&L on most intraday segments while keeping calendar violations at numerical zero and butterfly violations at the numerical floor; ex-post tails remain realistic and can be tuned through the CVaR weight. The five control heads admit clear economic semantics and analytic sensitivities, yielding a white-box learner that unifies pricing consistency and execution control in a reproducible pipeline. ...

DeltaHedge: A Multi-Agent Framework for Portfolio Options Optimization ArXiv ID: 2509.12753 “View on arXiv” Authors: Feliks Bańka, Jarosław A. Chudziak Abstract In volatile financial markets, balancing risk and return remains a significant challenge. Traditional approaches often focus solely on equity allocation, overlooking the strategic advantages of options trading for dynamic risk hedging. This work presents DeltaHedge, a multi-agent framework that integrates options trading with AI-driven portfolio management. By combining advanced reinforcement learning techniques with an ensembled options-based hedging strategy, DeltaHedge enhances risk-adjusted returns and stabilizes portfolio performance across varying market conditions. Experimental results demonstrate that DeltaHedge outperforms traditional strategies and standalone models, underscoring its potential to transform practical portfolio management in complex financial environments. Building on these findings, this paper contributes to the fields of quantitative finance and AI-driven portfolio optimization by introducing a novel multi-agent system for integrating options trading strategies, addressing a gap in the existing literature. ...

Controllable Generation of Implied Volatility Surfaces with Variational Autoencoders ArXiv ID: 2509.01743 “View on arXiv” Authors: Jing Wang, Shuaiqiang Liu, Cornelis Vuik Abstract This paper presents a deep generative modeling framework for controllably synthesizing implied volatility surfaces (IVSs) using a variational autoencoder (VAE). Unlike conventional data-driven models, our approach provides explicit control over meaningful shape features (e.g., volatility level, slope, curvature, term-structure) to generate IVSs with desired characteristics. In our framework, financially interpretable shape features are disentangled from residual latent factors. The target features are embedded into the VAE architecture as controllable latent variables, while the residual latent variables capture additional structure to preserve IVS shape diversity. To enable this control, IVS feature values are quantified via regression at an anchor point and incorporated into the decoder to steer generation. Numerical experiments demonstrate that the generative model enables rapid generation of realistic IVSs with desired features rather than arbitrary patterns, and achieves high accuracy across both single- and multi-feature control settings. For market validity, an optional post-generation latent-space repair algorithm adjusts only the residual latent variables to remove occasional violations of static no-arbitrage conditions without altering the specified features. Compared with black-box generators, the framework combines interpretability, controllability, and flexibility for synthetic IVS generation and scenario design. ...

Deep Learning vs. Black-Scholes: Option Pricing Performance on Brazilian Petrobras Stocks ArXiv ID: 2504.20088 “View on arXiv” Authors: Joao Felipe Gueiros, Hemanth Chandravamsi, Steven H. Frankel Abstract This paper explores the use of deep residual networks for pricing European options on Petrobras, one of the world’s largest oil and gas producers, and compares its performance with the Black-Scholes (BS) model. Using eight years of historical data from B3 (Brazilian Stock Exchange) collected via web scraping, a deep learning model was trained using a custom built hybrid loss function that incorporates market data and analytical pricing. The data for training and testing were drawn between the period spanning November 2016 to January 2025, using an 80-20 train-test split. The test set consisted of data from the final three months: November, December, and January 2025. The deep residual network model achieved a 64.3% reduction in the mean absolute error for the 3-19 BRL (Brazilian Real) range when compared to the Black-Scholes model on the test set. Furthermore, unlike the Black-Scholes solution, which tends to decrease its accuracy for longer periods of time, the deep learning model performed accurately for longer expiration periods. These findings highlight the potential of deep learning in financial modeling, with future work focusing on specialized models for different price ranges. ...

Towards a fast and robust deep hedging approach ArXiv ID: 2504.16436 “View on arXiv” Authors: Fabienne Schmid, Daniel Oeltz Abstract We present a robust Deep Hedging framework for the pricing and hedging of option portfolios that significantly improves training efficiency and model robustness. In particular, we propose a neural model for training model embeddings which utilizes the paths of several advanced equity option models with stochastic volatility in order to learn the relationships that exist between hedging strategies. A key advantage of the proposed method is its ability to rapidly and reliably adapt to new market regimes through the recalibration of a low-dimensional embedding vector, rather than retraining the entire network. Moreover, we examine the observed Profit and Loss distributions on the parameter space of the models used to learn the embeddings. The results show that the proposed framework works well with data generated by complex models and can serve as a construction basis for an efficient and robust simulation tool for the systematic development of an entirely model-independent hedging strategy. ...

Unbiased simulation of Asian options ArXiv ID: 2504.16349 “View on arXiv” Authors: Bruno Bouchard, Xiaolu Tan Abstract We provide an extension of the unbiased simulation method for SDEs developed in Henry-Labordere et al. [“Ann Appl Probab. 27:6 (2017) 1-37”] to a class of path-dependent dynamics, pertaining for Asian options. In our setting, both the payoff and the SDE’s coefficients depend on the (weighted) average of the process or, more precisely, on the integral of the solution to the SDE against a continuous function with bounded variations. In particular, this applies to the numerical resolution of the class of path-dependent PDEs whose regularity, in the sens of Dupire, is studied in Bouchard and Tan [“Ann. I.H.P., to appear”]. ...

A statistical technique for cleaning option price data ArXiv ID: 2501.11164 “View on arXiv” Authors: Unknown Abstract Recorded option pricing datasets are not always freely available. Additionally, these datasets often contain numerous prices which are either higher or lower than can reasonably be expected. Various reasons for these unexpected observations are possible, including human error in the recording of the details associated with the option in question. In order for the analyses performed on these datasets to be reliable, it is necessary to identify and remove these options from the dataset. In this paper, we list three distinct problems often found in recorded option price datasets alongside means of addressing these. The methods used are justified using sound statistical reasoning and remove option prices violating the standard assumption of no arbitrage. An attractive aspect of the proposed technique is that no option pricing model-based assumptions are used. Although the discussion is restricted to European options, the procedure is easily modified for use with exotic options as well. As a final contribution, the paper contains a link to six option pricing datasets which have already been cleaned using the proposed methods and can be freely used by researchers. ...

The AI Black-Scholes: Finance-Informed Neural Network ArXiv ID: 2412.12213 “View on arXiv” Authors: Unknown Abstract In the realm of option pricing, existing models are typically classified into principle-driven methods, such as solving partial differential equations (PDEs) that pricing function satisfies, and data-driven approaches, such as machine learning (ML) techniques that parameterize the pricing function directly. While principle-driven models offer a rigorous theoretical framework, they often rely on unrealistic assumptions, such as asset processes adhering to fixed stochastic differential equations (SDEs). Moreover, they can become computationally intensive, particularly in high-dimensional settings when analytical solutions are not available and thus numerical solutions are needed. In contrast, data-driven models excel in capturing market data trends, but they often lack alignment with core financial principles, raising concerns about interpretability and predictive accuracy, especially when dealing with limited or biased datasets. This work proposes a hybrid approach to address these limitations by integrating the strengths of both principled and data-driven methodologies. Our framework combines the theoretical rigor and interpretability of PDE-based models with the adaptability of machine learning techniques, yielding a more versatile methodology for pricing a broad spectrum of options. We validate our approach across different volatility modeling approaches-both with constant volatility (Black-Scholes) and stochastic volatility (Heston), demonstrating that our proposed framework, Finance-Informed Neural Network (FINN), not only enhances predictive accuracy but also maintains adherence to core financial principles. FINN presents a promising tool for practitioners, offering robust performance across a variety of market conditions. ...