Risk-Regularized Deep Learning for Hedged Option Portfolios

Summary

This study presents a historical-data-based deep learning framework for systematic options trading that incorporates portfolio risk sensitivities directly into training. Its objective combines a performance-oriented loss with a differentiable penalty for exposure to selected risk factors. This encourages the learned portfolio to meet chosen hedging constraints while optimizing risk-adjusted returns, without relying on simulated market dynamics to learn a hedging policy.

The framework is evaluated on static delta-neutral straddle portfolios in Nasdaq 100 equity options, with penalties targeting first-order directional exposure. The authors compare an exposure-normalized penalty and a Greek-ratio drift penalty. They report that suitable regularization improves out-of-sample risk-adjusted performance versus an unregularized baseline while lowering realized directional exposure. The evidence is limited to the described portfolio and market; the document does not state the sample period, performance metrics, penalty calibration details, or transaction-cost treatment.

Key ideas

• The training objective combines return optimization with a differentiable penalty on selected portfolio risk exposures.
• The framework learns from historical data rather than simulated market dynamics.
• The implementation studies static delta-neutral straddle portfolios in Nasdaq 100 options.
• Two penalty designs target first-order directional exposure.
• The reported calibrated penalties improve out-of-sample risk-adjusted performance and reduce realized directional exposure.

Tags

# Taming the Greeks: Option Portfolios with Inductive Biases


# Taming the Greeks: Option Portfolios with Inductive Biases









We present an end-to-end deep learning framework for systematic options trading that directly embeds hedging behavior through explicit control of portfolio-level risk exposures. While neural networks trained to optimize risk-adjusted performance have been shown to outperform traditional rules-based strategies, such approaches remain agnostic to the sensitivities of the resulting portfolios with respect to specific underlying risk factors. We propose a general training objective that combines a performance-driven loss with a differentiable risk-sensitivity penalty, enforcing neutrality to selected risk dimensions. Unlike reinforcement learning methods that approximate optimal hedging policies via simulated market dynamics, our framework operates entirely on historical data and jointly optimizes risk-adjusted returns and targeted risk constraints in a single learning problem. We instantiate the framework on static delta-neutral straddle portfolios with the penalty directed at first-order directional exposure, and evaluate two penalty variants -- an exposure-normalized penalty and a Greek-ratio drift penalty. Empirical results on Nasdaq 100 equity options demonstrate that appropriately calibrated regularization simultaneously improves out-of-sample risk-adjusted performance relative to an unregularized baseline while reducing realized directional exposure.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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