Deep Hedging

Deep Hedging with Reinforcement Learning: A Practical Framework for Option Risk Management ArXiv ID: 2512.12420 “View on arXiv” Authors: Travon Lucius, Christian Koch, Jacob Starling, Julia Zhu, Miguel Urena, Carrie Hu Abstract We present a reinforcement-learning (RL) framework for dynamic hedging of equity index option exposures under realistic transaction costs and position limits. We hedge a normalized option-implied equity exposure (one unit of underlying delta, offset via SPY) by trading the underlying index ETF, using the option surface and macro variables only as state information and not as a direct pricing engine. Building on the “deep hedging” paradigm of Buehler et al. (2019), we design a leak-free environment, a cost-aware reward function, and a lightweight stochastic actor-critic agent trained on daily end-of-day panel data constructed from SPX/SPY implied volatility term structure, skew, realized volatility, and macro rate context. On a fixed train/validation/test split, the learned policy improves risk-adjusted performance versus no-hedge, momentum, and volatility-targeting baselines (higher point-estimate Sharpe); only the GAE policy’s test-sample Sharpe is statistically distinguishable from zero, although confidence intervals overlap with a long-SPY benchmark so we stop short of claiming formal dominance. Turnover remains controlled and the policy is robust to doubled transaction costs. The modular codebase, comprising a data pipeline, simulator, and training scripts, is engineered for extensibility to multi-asset overlays, alternative objectives (e.g., drawdown or CVaR), and intraday data. From a portfolio management perspective, the learned overlay is designed to sit on top of an existing SPX or SPY allocation, improving the portfolio’s mean-variance trade-off with controlled turnover and drawdowns. We discuss practical implications for portfolio overlays and outline avenues for future work. ...

Deep Hedging to Manage Tail Risk ArXiv ID: 2506.22611 “View on arXiv” Authors: Yuming Ma Abstract Extending Buehler et al.’s 2019 Deep Hedging paradigm, we innovatively employ deep neural networks to parameterize convex-risk minimization (CVaR/ES) for the portfolio tail-risk hedging problem. Through comprehensive numerical experiments on crisis-era bootstrap market simulators – customizable with transaction costs, risk budgets, liquidity constraints, and market impact – our end-to-end framework not only achieves significant one-day 99% CVaR reduction but also yields practical insights into friction-aware strategy adaptation, demonstrating robustness and operational viability in realistic markets. ...

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. ...

Deep Hedging of Green PPAs in Electricity Markets ArXiv ID: 2503.13056 “View on arXiv” Authors: Unknown Abstract In power markets, Green Power Purchase Agreements have become an important contractual tool of the energy transition from fossil fuels to renewable sources such as wind or solar radiation. Trading Green PPAs exposes agents to price risks and weather risks. Also, developed electricity markets feature the so-called cannibalisation effect : large infeeds induce low prices and vice versa. As weather is a non-tradable entity the question arises how to hedge and risk-manage in this highly incom-plete setting. We propose a ‘‘deep hedging’’ framework utilising machine learning methods to construct hedging strategies. The resulting strategies outperform static and dynamic benchmark strategies with respect to different risk measures. ...

CoFinDiff: Controllable Financial Diffusion Model for Time Series Generation ArXiv ID: 2503.04164 “View on arXiv” Authors: Unknown Abstract The generation of synthetic financial data is a critical technology in the financial domain, addressing challenges posed by limited data availability. Traditionally, statistical models have been employed to generate synthetic data. However, these models fail to capture the stylized facts commonly observed in financial data, limiting their practical applicability. Recently, machine learning models have been introduced to address the limitations of statistical models; however, controlling synthetic data generation remains challenging. We propose CoFinDiff (Controllable Financial Diffusion model), a synthetic financial data generation model based on conditional diffusion models that accept conditions about the synthetic time series. By incorporating conditions derived from price data into the conditional diffusion model via cross-attention, CoFinDiff learns the relationships between the conditions and the data, generating synthetic data that align with arbitrary conditions. Experimental results demonstrate that: (i) synthetic data generated by CoFinDiff capture stylized facts; (ii) the generated data accurately meet specified conditions for trends and volatility; (iii) the diversity of the generated data surpasses that of the baseline models; and (iv) models trained on CoFinDiff-generated data achieve improved performance in deep hedging task. ...

A New Way: Kronecker-Factored Approximate Curvature Deep Hedging and its Benefits ArXiv ID: 2411.15002 “View on arXiv” Authors: Unknown Abstract This paper advances the computational efficiency of Deep Hedging frameworks through the novel integration of Kronecker-Factored Approximate Curvature (K-FAC) optimization. While recent literature has established Deep Hedging as a data-driven alternative to traditional risk management strategies, the computational burden of training neural networks with first-order methods remains a significant impediment to practical implementation. The proposed architecture couples Long Short-Term Memory (LSTM) networks with K-FAC second-order optimization, specifically addressing the challenges of sequential financial data and curvature estimation in recurrent networks. Empirical validation using simulated paths from a calibrated Heston stochastic volatility model demonstrates that the K-FAC implementation achieves marked improvements in convergence dynamics and hedging efficacy. The methodology yields a 78.3% reduction in transaction costs ($t = 56.88$, $p < 0.001$) and a 34.4% decrease in profit and loss (P&L) variance compared to Adam optimization. Moreover, the K-FAC-enhanced model exhibits superior risk-adjusted performance with a Sharpe ratio of 0.0401, contrasting with $-0.0025$ for the baseline model. These results provide compelling evidence that second-order optimization methods can materially enhance the tractability of Deep Hedging implementations. The findings contribute to the growing literature on computational methods in quantitative finance while highlighting the potential for advanced optimization techniques to bridge the gap between theoretical frameworks and practical applications in financial markets. ...

Deep Hedging Bermudan Swaptions ArXiv ID: 2411.10079 “View on arXiv” Authors: Unknown Abstract Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero transaction costs, perfect liquidity, and continuous-time hedging, which often differ from real market environments. This discrepancy can lead to residual profit and loss (P&L), resulting in two primary issues. First, residual P&L may prevent achieving the initial model price, especially with improper parameter settings, potentially causing a negative P&L trend and significant financial impacts. Second, controlling the distribution of residual P&L to mitigate downside risk is challenging, as hedged positions may become curve gamma-short, making them vulnerable to large interest rate movements. The deep hedging approach enables flexible selection of convex risk measures and hedge strategies, allowing for improved residual P&L management. This study also addresses challenges in applying the deep hedging approach to Bermudan swaptions, such as efficient arbitrage-free market scenario generation and managing early exercise conditions. Additionally, we introduce a unique “Option Spread Hedge” strategy, which allows for robust hedging and provides intuitive interpretability. Numerical analysis results demonstrate the effectiveness of our approach. ...

Fast Deep Hedging with Second-Order Optimization ArXiv ID: 2410.22568 “View on arXiv” Authors: Unknown Abstract Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may be delicate and suffer from slow convergence, particularly for options with long maturities and complex sensitivities to market parameters. To address this, we propose a second-order optimization scheme for deep hedging. We leverage pathwise differentiability to construct a curvature matrix, which we approximate as block-diagonal and Kronecker-factored to efficiently precondition gradients. We evaluate our method on a challenging and practically important problem: hedging a cliquet option on a stock with stochastic volatility by trading in the spot and vanilla options. We find that our second-order scheme can optimize the policy in 1/4 of the number of steps that standard adaptive moment-based optimization takes. ...

Is the difference between deep hedging and delta hedging a statistical arbitrage? ArXiv ID: 2407.14736 “View on arXiv” Authors: Unknown Abstract The recent work of Horikawa and Nakagawa (2024) claims that under a complete market admitting statistical arbitrage, the difference between the hedging position provided by deep hedging and that of the replicating portfolio is a statistical arbitrage. This raises concerns as it entails that deep hedging can include a speculative component aimed simply at exploiting the structure of the risk measure guiding the hedging optimisation problem. We test whether such finding remains true in a GARCH-based market model, which is an illustrative case departing from complete market dynamics. We observe that the difference between deep hedging and delta hedging is a speculative overlay if the risk measure considered does not put sufficient relative weight on adverse outcomes. Nevertheless, a suitable choice of risk measure can prevent the deep hedging agent from engaging in speculation. ...

Experimental Analysis of Deep Hedging Using Artificial Market Simulations for Underlying Asset Simulators ArXiv ID: 2404.09462 “View on arXiv” Authors: Unknown Abstract Derivative hedging and pricing are important and continuously studied topics in financial markets. Recently, deep hedging has been proposed as a promising approach that uses deep learning to approximate the optimal hedging strategy and can handle incomplete markets. However, deep hedging usually requires underlying asset simulations, and it is challenging to select the best model for such simulations. This study proposes a new approach using artificial market simulations for underlying asset simulations in deep hedging. Artificial market simulations can replicate the stylized facts of financial markets, and they seem to be a promising approach for deep hedging. We investigate the effectiveness of the proposed approach by comparing its results with those of the traditional approach, which uses mathematical finance models such as Brownian motion and Heston models for underlying asset simulations. The results show that the proposed approach can achieve almost the same level of performance as the traditional approach without mathematical finance models. Finally, we also reveal that the proposed approach has some limitations in terms of performance under certain conditions. ...