标题： 用五阶波动率模型捕捉微笑动态：标普500指数，偏斜-粘性比率和VIX 显示英文标题

标题： Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX

摘要： 我们引入了双因子五次Ornstein-Uhlenbeck模型，其中波动率被建模为基于两个由相同布朗运动驱动的Ornstein-Uhlenbeck过程之和的五次多项式，每个过程以不同的速度均值回归。 我们证明了五次模型能够有效捕捉SPX和VIX的波动率曲面，同时在从几天到超过两年的不同期限范围内与偏斜粘性比率（SSR）一致。 此外，五次模型与关键的经验特征事实保持一致，特别是再现了Zumbach效应。 显示英文摘要

摘要： We introduce the two-factor Quintic Ornstein-Uhlenbeck model, where volatility is modeled as a polynomial of degree five based on the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian Motion, each mean-reverting at a different speed. We demonstrate that the Quintic model effectively captures the volatility surfaces of SPX and VIX while aligning with the skew-stickiness ratio (SSR) across maturities ranging from a few days to over two years. Furthermore, the Quintic model shows consistency with key empirical stylized facts, notably reproducing the Zumbach effect.