Risk-Sensitive Option Market Making with Arbitrage-Free eSSVI Surfaces: A Constrained RL and Stochastic Control Bridge

2025-10-06

AI Summary

This paper formulates options market making as a risk-sensitive, joint control problem subject to static no-arbitrage constraints, unifying quote execution, dynamic hedging, and implied volatility surface evolution. Method: (1) A differentiable eSSVI surface layer is introduced, coupled with state-dependent Lagrange multipliers to rigorously eliminate butterfly and calendar arbitrage; (2) a five-component trading strategy architecture with economic interpretability is designed, enabling analytical sensitivity computation and transparent, white-box decision-making; (3) a differentiable CVaR objective—implemented via the Rockafellar–Uryasev representation—is adopted for tail-risk management, optimized using a hybrid policy gradient algorithm combining pathwise derivatives and likelihood ratio estimation. Results: Empirical evaluation shows near-zero arbitrage violations, intraday positive risk-adjusted P&L across most trading hours, controllable tail distribution preserving realistic market characteristics, and establishes the first end-to-end, reproducible, no-arbitrage-aware reinforcement learning market making framework.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Sequential Decision Making
• Machine Learning: Reinforcement Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Formulating option market making as constrained risk-sensitive control problem
• Enforcing static no-arbitrage conditions via differentiable eSSVI surfaces
• Optimizing execution, hedging, and surface deformations with CVaR objective

Innovation

• Arbitrage-free eSSVI surfaces enforce static constraints
• Differentiable CVaR objective shapes tail risk management
• Constrained RL unifies pricing, hedging, and execution control