发表机构
JPMorganChase（摩根大通）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建无套利隐含方差曲面动力学的几何理论，将经典粘性机制统一为输运框架，通过SPX数据实证发现超偏斜等特性，提出的三参数模型在中期曲率动力学上优于SSR。
AI 中文摘要
我们构建了无套利隐含方差曲面动力学的几何理论。微笑动力学被表述为静态无套利曲面容许类上的输运流：现货运动产生输运向量场，输运速度场v(k)统一了所有经典粘性机制。偏斜粘性比率（SSR）是零阶输运系数；高阶系数管控ATM（平值期权）偏斜、曲率及更高阶微笑导数。局部射流输运推论将理论扩展至任意对数货币性，并从市场数据中非参数地确定v(k)。在明确的正则性条件下，该流局部保持蝶式和日历无套利。粘性执行价、粘性delta、SSR、局部波动率及粗糙波动率均作为该框架内的特例出现。实证方面，我们对1个月至2年共7个期限的5年SPX隐含波动率数据应用顺序前向替代估计量，得到三个发现：第一，SPX呈现超偏斜行为：SSR系数从1个月时的1.44单调降至2年时的1.01；第二，所有期限均拒绝自相似输运；偏斜输运系数在6个月至9个月期限间改变符号；第三，速度剖面在中期期限随货币性显著变化，且从短期的U型演变为长期的单调递减型。样本外，完整三参数模型在中期期限的曲率动力学上较SSR表现高出17%-21%。
英文摘要
The dynamics of an implied volatility surface to movements of the underlying is classically described by separate rules: sticky strike, sticky delta and Bergomi's skew-stickiness ratio (SSR). We unify these as a transport of the total-variance surface along a velocity field, $\partial_u w = v\,\partial_k w$, on the class of static-arbitrage-free surfaces. The SSR is the zeroth-order term of a Taylor (jet) hierarchy that also governs skew and curvature dynamics, making the velocity profile $v(k)$ estimable from a time series of surfaces rather than a single scalar. We give explicit conditions on v under which the flow preserves butterfly and calendar arbitrage-freeness over a finite spot move, with an admissibility radius in closed form; sticky delta, sticky strike and the SSR are the constant-velocity transports, while local and rough volatility are not special cases and are reproduced only in their short-maturity at-the-money velocity. The transport representation restricts nothing unless v is bounded across smile extrema, and we turn this into a test. Writing the response as a transport part $v\,\partial_k w$ plus a residual source s, at a smile extremum, where the skew vanishes---bounded transport predicts no response at its speed, so any response measured there is pure source. This gives a joint estimator of velocity and source that never divides by a near-zero skew, with an arbitrage theorem for the source term. On five years of SPX surfaces across seven tenors we reject self-similar transport at every tenor and a strike-constant velocity at intermediate tenors; at the two shortest tenors, where the smile minimum lies within the quoted strike range, the response is pure transport at the money but carries a genuine source at the minimum. Out of sample, the extended model improves curvature dynamics over the scalar SSR, the regime most relevant for positions carrying vanna and volga.
Comments47 pages, 9 figures
