call spread replication

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 paper addresses static fixed-income pricing and liability cash-flow replication by developing a model-free no-arbitrage framework. Methodologically, it rigorously establishes that static no-arbitrage is equivalent to the existence of a strictly positive discount curve that exactly reproduces all market quotes; integrates static arbitrage analysis, convex optimization, and measure-theoretic pricing; and systematically studies exact and super-replication of liabilities. Key contributions include: (i) the first necessary and sufficient condition for the existence of a minimum-cost super-replicating portfolio; and (ii) the first rigorous theoretical foundation for static swap–repo replication. The framework unifies discount-curve construction with liability-driven investing, thereby enhancing robustness, interpretability, and operational feasibility in liability matching—directly supporting economic capital calculation and regulatory practice. (149 words)

Recovering the implied risk-neutral density from irregular option quotes is highly ill-posed, making stable estimation challenging even with accurate price data. This study systematically evaluates multiple methods on both synthetic and real-market (NIFTY) benchmarks, exposing the inherent numerical instability of the problem and introducing the concept of “target-dependent inductive bias” to tailor estimators to specific objectives. Combining a two-component lognormal mixture model, DeepONet, a Quote Transformer, SVI parametrization, and test-time adaptation strategies, experiments demonstrate that the mixture model achieves the lowest aggregate error on synthetic data, while DeepONet reduces tail and variance errors by over 34%. Incorporating test-time adaptation further decreases DeepONet’s RMSE by 28.3% on NIFTY data, substantially enhancing its generalization performance.

This study addresses the reproducibility challenges of the multi-market fragmentation and delayed arbitrage agent-based model proposed by Wah and Wellman (2016), which stemmed from insufficient implementation details and limited quantitative reporting. Leveraging the authors’ subsequently released code, we formalize the modeling process using the ODD protocol and enhance statistical robustness by increasing simulation runs and applying bootstrapping to construct confidence intervals. Our replication achieves relational equivalence across most metrics but rejects quantitative alignment under non-zero delay conditions. Notably, we uncover that conclusions regarding fragmentation effects are highly sensitive to the specific implementation of greedy strategies; under alternative strategies, market fragmentation actually reduces execution time and improves trader welfare. This work thus provides the first complete and transparent replication framework for the original model.

This study addresses the challenge of simultaneously achieving precise local shape control and strict static no-arbitrage compliance in implied volatility curve modeling. To this end, it proposes a parsimonious and interpretable parametric approach grounded in the risk-neutral distribution. By introducing parameters that exhibit stable cross-maturity patterns, the method directly governs local curvature characteristics—such as convexity and concavity—while inherently satisfying no-arbitrage constraints. The resulting model flexibly accommodates diverse curvature patterns and supports both term structure interpolation and dynamic modeling. Empirical validation on a two-year dataset of S&P 500 options, encompassing over 250,000 calibrated volatility curves, demonstrates the stability, generalizability, and high fidelity of the proposed parameterization in capturing complex market dynamics.

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.

This work addresses the circular dependency between implied volatility and market prices that hinders high-fidelity synthetic option data generation. The authors propose an end-to-end framework that integrates a jump hidden Markov model to simulate multi-asset price paths and a state-dependent extension of the Heston model to intrinsically generate implied volatility surfaces without external calibration. American options are priced via a recombinant binomial tree, thereby breaking the circularity. By innovatively coupling the jump HMM with the state-dependent Heston process, the model naturally reproduces volatility smiles, skews, and term structures. A hierarchical neural surrogate further enhances cross-asset generalization. Experiments demonstrate robust generation of realistic synthetic data across diverse market regimes, accurately capturing implied volatility surfaces, path-conditioned Greeks, and short-dated premium dynamics. The implementation is publicly released as a Julia package.

This study addresses the challenge of enforcing no-arbitrage constraints in modeling option-implied information—specifically, implied densities and implied volatility—by proposing a shallow neural network approach. The method reinterprets implied volatility as a differentiable, pointwise correction mapping from the Black–Scholes pseudo-density to the risk-neutral density and jointly models both quantities by embedding differentiable no-arbitrage constraints directly into the architecture. The work introduces the first shallow neural representation framework that intrinsically incorporates no-arbitrage conditions, demonstrating that deep networks are unnecessary for this task. Empirical results show that a single-hidden-layer network efficiently and accurately approximates both implied densities and implied volatility, outperforming deeper or wider architectures in terms of both accuracy and computational efficiency.

Prediction markets often treat prices directly as probabilities, yet systematic biases persist in practice. Drawing on 23 million sports-related trades from the Kalshi platform, this study employs time-stratified calibration models, fits Prelec probability weighting functions, and compares prices across single- and multi-leg parlays to uncover two key findings: first, calibration bias evolves dynamically with time to expiration, exhibiting a step-like convergence near settlement; second, multi-leg parlays display a systematic premium independent of single-leg calibration, with the premium increasing monotonically with the number of legs. These results underscore that accurate probability estimation in prediction markets must jointly account for time to expiration and contract structure, offering new empirical evidence and a refined framework for understanding market pricing mechanisms.

This work proposes a data-driven approach based on symbolic regression to automatically discover concise and highly accurate parametric expressions for the implied volatility surface. The method directly searches market data for analytical forms of total implied variance as a function of log-moneyness and time to maturity, without assuming any predefined functional structure. As the first application of symbolic regression to implied volatility modeling, the resulting formulas are both interpretable and compact, achieving fitting accuracy and model parsimony that rival or even surpass those of the widely used Stochastic Volatility Inspired (SVI) framework.