Risk-Sensitive Option Market Making with Arbitrage-Free eSSVI Surfaces: A Constrained RL and Stochastic Control Bridge
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908577440989184 |
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| author | Zhang, Jian'an |
| author_facet | Zhang, Jian'an |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Risk-Sensitive Option Market Making with Arbitrage-Free eSSVI Surfaces: A Constrained RL and Stochastic Control Bridge Zhang, Jian'an Trading and Market Microstructure 68T05, 90C20, 91G20 I.2.6; I.2.8; G.3 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. |
| title | Risk-Sensitive Option Market Making with Arbitrage-Free eSSVI Surfaces: A Constrained RL and Stochastic Control Bridge |
| topic | Trading and Market Microstructure 68T05, 90C20, 91G20 I.2.6; I.2.8; G.3 |
| url | https://arxiv.org/abs/2510.04569 |