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Hao Qin, Ruozhong Yang, Charlie Che, Liming Feng · 2026-07-07
The paper introduces a way to turn a set of arbitrage-free option prices into full risk-neutral probability distributions (marginals) for the underlying asset. It assigns probability mass strike-by-strike to exactly match observed prices, and uses closed-form power-law tails beyond the observed strike range, guaranteeing no butterfly or calendar arbitrage while allowing easy computation of densities, quantiles, and Monte Carlo sampling.
Why it matters: Practitioners who build models from option-implied distributions — for tail-risk measurement, scenario analysis, or volatility calibration — could use this as a clean, arbitrage-consistent input. It aims to close the gap between raw option prices and the usable probability distributions many downstream methods require, and was tested on S&P 500 data.
⚠ This is a computational/methodological tool requiring clean arbitrage-free option-price inputs, not a trading strategy, and its usefulness depends on the quality of the downstream application.
Many quantitative finance methods and applications are formulated in terms of option-implied risk-neutral marginals rather than directly in terms of option prices. Representative examples include martingale optimal transport, Bass local-volatility calibration, scenario analysis, and option-implied tail-risk measurement. The desired risk-neutral marginals should define a genuine probability law on the entire support, reproduce the input arbitrage-free option prices exactly, be free of butterfly and calendar arbitrage, and admit efficient evaluation of the density, distribution function, and quantiles, as well as Monte Carlo sampling. Existing methods typically optimize only a subset of these properties, depending on their intended purpose. This leaves a gap between upstream arbitrage-free option prices and the readily usable risk-neutral marginals required by downstream applications. We propose an explicit construction of risk-neutral marginals from discrete arbitrage-free option prices. On the observed strike range, probability mass is assigned interval by interval to exactly reproduce the input option prices. Outside the observed range, closed-form power-law tails complete the distribution by satisfying price and slope boundary conditions and allocating the remaining probability mass. Butterfly- and calendar-arbitrage-freeness are guaranteed by construction. The construction is feasible by design and computationally efficient. The resulting marginal laws admit closed-form densities, distribution functions, quantiles, and efficient Monte Carlo sampling. Numerical experiments on synthetic SSVI data and S\&P~500 market data demonstrate that the proposed construction efficiently and robustly produces marginals satisfying all of these properties in practice.
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AI summary generated from the paper’s public abstract via arXiv; it may miss nuance — read the source before relying on it. Thank you to arXiv for its open-access interoperability; StockTools is not affiliated with arXiv, and all rights remain with the authors. Educational only, not financial advice.