compute arbitrage-free prices

This paper addresses the challenge of constructing arbitrage-free option price surfaces from noisy market quotes. We propose a robust modeling framework grounded in Chebyshev tensor bases and Hamiltonian energy-driven dynamics. Our key contribution is the introduction of a “risk-neutral density fog”—a locally adjustable deviation variable—regularized via a Hamiltonian-type energy functional to enable controlled local corrections while enforcing global no-arbitrage constraints. The method integrates spectral regularization, transport-inspired regularization, and static no-arbitrage constraints into a jointly convex optimization problem, efficiently solved using the OSQP solver. Empirical evaluation demonstrates that the approach achieves 98–99% bid-ask spread coverage under stable market conditions, with static arbitrage violation rates below 1%. Crucially, it preserves surface smoothness and economic plausibility even under market stress, substantially enhancing model robustness and practical applicability.

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.

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.

This study addresses the pricing inconsistency between bivariate interest rate exotic derivatives—such as CMS spread options—and their two underlying CMS options observed in the market. To resolve this, the authors develop a unified arbitrage-free pricing framework by formulating and solving the dual Lagrangian of a constrained Schrödinger optimal transport problem. This work represents the first application of constrained optimal transport theory to achieve cross-market consistency in interest rate derivative pricing. The proposed framework guarantees that the prices of exotic instruments remain compatible with observable market data while efficiently computing their no-arbitrage price bounds. Numerical experiments demonstrate the method’s practical feasibility, robustness, and computational efficiency in real-world pricing scenarios.

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 existing consistency conditions for multi-maturity option prices under bounded bid–ask spreads are sufficient to preclude model-free arbitrage. By refining the definition of admissible quotes and integrating the completeness condition for single-maturity options, the authors construct the first minimal two-maturity counterexample that satisfies all known consistency conditions yet admits a pathwise arbitrage, thereby disproving the sufficiency conjecture of Gerhold and Gülüm. Furthermore, employing techniques such as convex envelopes, concave maximization, and extremal envelopes within the geometry of bounded spreads, they explicitly derive closed-form two-maturity basket operators, precisely characterize the model-free arbitrage cone, and uncover a high-dimensional open region of admissible quotes generated by the counterexample, fully describing the structure of two-maturity executable, arbitrage-free markets.

This work addresses the challenge of accurately identifying optimal policies and active constraints when both are unknown. It proposes a unified simulation-grid-based dual framework that integrates Fenchel duality, Doob martingale compensation, complementary slackness, and occupancy-measure weighting. By decomposing residuals via conditional budget identities and leveraging Bellman curvature, the method constructs a tight policy region without requiring a reference solution. It simultaneously estimates policy error, certifies active constraint facets, and provides joint verification of value bounds and policy distance. Empirical results demonstrate its ability to achieve full coverage in auditing external policy errors, deliver zero false positives in active facet detection, maintain tightness in 50-dimensional asset stress tests, and reveal that dual-learning accuracy becomes the performance bottleneck in high dimensions.

This work establishes a unified theoretical framework for implied, local, and learned volatility surfaces under strict no-arbitrage constraints, enabling dynamic modeling and learning. By introducing an infinite-dimensional state-space geometric structure for the volatility surface, it disentangles static no-arbitrage conditions from dynamic evolution mechanisms. The approach integrates Hilbert space dynamics, the Musiela maturity-forward transport identity, and Dupire’s local variance geometry to achieve exact modal reduction and closed-form truncation error bounds. Innovatively combining neural operators with normalizing flows, the framework ensures universal approximation while preserving no-arbitrage properties, and introduces a falsifiable empirical protocol. It further derives the covariance-optimal hedging strategy α* = (HᵀC H)⁻¹HᵀCν and exact change-of-variable formulas linking exponential local variance flows to price simplex flows, thereby supporting autonomous finite-dimensional controlled simulations.

Traditional no-arbitrage bounds are frequently violated in prediction markets; however, such deviations are not necessarily exploitable due to operational constraints imposed by trading protocols. This work disentangles the no-arbitrage condition from protocol executability for the first time, introducing the concept of “executable arbitrage.” By integrating on-chain transaction data, smart contract conversion tracking, and order book modeling, the study reconstructs the value of executable portfolios. A bidirectional NegRisk Adapter prototype is developed to empirically identify $1.12 million in executable arbitrage profits—of which $1.086 million stems from converter strategies—and demonstrates that protocol-supported operations significantly narrow arbitrage windows and enhance market efficiency.