no-arbitrage constraints

This study addresses the monotonicity of normalized implied volatility coordinates within a finite quoted option chain under no-arbitrage conditions and derives model-independent variance identities. Relying solely on static no-arbitrage assumptions—including discrete strike comparisons, convexity, monotonicity, and call-put parity—the authors provide the first purely discrete proof of monotonicity for normalized coordinates in both the Black–Scholes and Bachelier frameworks, without requiring continuous quotes or differentiability. The main contributions are twofold: (1) a rigorous discrete verification of monotonicity in these two canonical implied volatility models, and (2) the introduction of a normal variance identity that serves as the natural counterpart to Fukasawa’s log-normal result, thereby establishing a model-independent theoretical foundation for volatility derivatives.

This study addresses the challenge of constructing option price surfaces that are simultaneously smooth and strictly arbitrage-free across both time-to-maturity and strike dimensions. To this end, the authors propose an efficient and flexible nonparametric method that directly calibrates to market quotes via linear programming, ensuring smoothness and absence of arbitrage under only simple positivity constraints, while naturally accommodating bid–ask spread bounds. The key innovation lies in the introduction of an equivalent parametrization in terms of positive “discrete local volatility,” which substantially simplifies the constraint structure. Compared to existing approaches that fit implied volatility surfaces, the proposed method significantly reduces computational cost and demonstrates strong empirical performance and practicality when applied to S&P 500 index option data.

Joint modeling of the SPX and VIX term structures faces challenges in simultaneously satisfying static arbitrage constraints (calendar, vertical, butterfly), monotonicity, and Lipschitz continuity. Method: We propose ARBITER, the first risk-neutral neural operator explicitly embedding financial physical constraints—via a constrained decoder, outer-gradient updates, and projection-based enforcement—to jointly generate arbitrage-free implied volatility and variance curves within an operator learning framework. Contribution/Results: ARBITER innovatively couples neural operators with multiple static arbitrage constraints and introduces novel evaluation metrics—Dual-Gap and No-Arbitrage Index (NI)—to rigorously quantify constraint satisfaction. Empirical results demonstrate that ARBITER significantly outperforms Fourier Neural Operators and DeepONet in calibration stability, long-horizon extrapolation accuracy, and generalization across market regimes. It provides a verifiable, production-ready, no-arbitrage solution for dynamic volatility surface modeling.

This paper investigates whether embedding no-arbitrage constraints as soft penalties into a reinforcement learning (RL) world model for volatility surface modeling effectively aligns high-capacity agents’ behavior—or instead induces Goodhart-type misuse. Method: We construct a convex-geometric volatility manifold, model market dynamics via RNNs, and introduce differentiable no-arbitrage penalties alongside a Goodhart decomposition, optimizing policies with PPO. Contributions/Results: We propose the “law-strength frontier” and the “Graceful Failure Index” (GFI) to characterize the trade-off between penalty strength and reward; prove a No-Free-Lunch theorem for “law-seeking learning,” showing it cannot simultaneously outperform structured baselines across reward, penalty adherence, and robustness; and empirically validate—on SPX/VIX-like environments—that all law-seeking RL agents underperform simple structural strategies, clustering in high-penalty, high-GFI regimes, thereby confirming theoretical performance limits.

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.

Existing methods struggle to construct risk-neutral marginal distributions from arbitrage-free option prices that simultaneously satisfy no butterfly arbitrage, no calendar spread arbitrage, exact market price recovery, efficient sampling, and full support. This work proposes an explicit construction method that exactly fits observed option prices within the range of quoted strikes via piecewise probability mass allocation, while extrapolating beyond this range using closed-form power-law tails that satisfy necessary boundary conditions. The approach uniquely achieves, within a unified framework, strict absence of static arbitrage, exact calibration to market prices, analytical expressions for both density and quantile functions, and efficient Monte Carlo sampling. Experiments on synthetic SSVI surfaces and S&P 500 market data demonstrate its computational efficiency, robustness, and practical utility, effectively bridging the gap between option pricing models and downstream applications.

This work addresses arbitrage opportunities in data markets arising from the replicability of information products, where buyers can reconstruct high-value information by combining cheaper offerings, thereby undermining seller revenue. The paper unifies query and model pricing as instances of information pricing and introduces no-arbitrage constraints within a Bayesian decision framework for buyer valuation. It innovatively integrates Bayesian value assessment with Blackwell dominance theory to characterize no-arbitrage conditions across both pricing paradigms. Under a threshold utility assumption, the analysis leverages the Blackwell order of information structures to derive structural insights. To tackle computational challenges, the authors design a branch-and-bound algorithm based on McCormick relaxations, enabling the construction of revenue-maximizing, no-arbitrage pricing mechanisms over restricted menus—offering both theoretical grounding and practical solutions for data market design.

This study investigates whether a universally profitable trading strategy exists across all market trajectories. By integrating measure theory, combinatorics, and computability theory—alongside the no-arbitrage principle, the no-free-lunch theorem, and Turing-style diagonalization—it constructs an adversarial market model and establishes an analogy between financial martingales and thermodynamic detailed balance. Employing tools such as equivalent martingale measures, combinatorial averaging, and Cantor diagonalization, the paper demonstrates that any practically effective trading strategy must rely on specific assumptions about market states, and its automated execution systematically amplifies tail risk. The work thereby theoretically refutes the feasibility of universal trading strategies in competitive markets and reveals fundamental limits to their generalizability.

This study addresses the challenge of robustly extracting risk-neutral densities from near-expiry options, which is hindered by low premiums, wide bid–ask spreads, and asynchronous quotes that undermine conventional approaches. To overcome these issues, the authors propose a model-free two-stage framework: first, the ARIES strategy eliminates static arbitrage opportunities under market depth constraints; second, the SEDEx method recovers the density by incorporating smoothness and maximum entropy principles while respecting bid–ask bounds. Notably, this approach explicitly treats the bid–ask spread as a fundamental market constraint and uniquely integrates executable arbitrage filtering with entropy regularization, substantially enhancing stability in processing short-dated option data. Empirical validation on both synthetic Heston-generated data and real-world SPX options demonstrates the method’s ability to reconstruct stable and accurate implied volatility smiles.

Standard jump-diffusion models assume independence between jump and diffusion components, failing to capture empirical evidence that jump occurrences and sizes depend dynamically on contemporaneous diffusion behavior. Method: We propose a novel arbitrage-free multi-type jump-diffusion framework featuring a bidirectional (upward/downward) diffusion-triggered jump mechanism—where jump intensity and magnitude are state-dependent on both the direction and magnitude of the underlying diffusion process. Using the Girsanov theorem and a normalized Esscher transform, we derive explicit no-arbitrage conditions that unify physical drift, model parameters, and market risk premia. Contribution/Results: The framework eliminates arbitrage opportunities inherent in conventional specifications and provides theoretically grounded, analytically tractable closed-form pricing formulas for volatility-sensitive derivatives. Empirically, it significantly enhances modeling fidelity for nonlinear jump dynamics and improves out-of-sample pricing performance.