在波动率微笑的动态研究中，以下信息息息相关，一脉相承。
Implied Vol是Local Vol的路径平均
Implied Vol的曲面斜率是Local Vol的一半。
ATM Implied Vol = ATM Local Vol
Local Vol之下的ATM Implied Vol对Ln F的回归系数是Implied Vol曲面斜率的2倍，即the Rule of Two。
Bergomi 2009 SSR (Skew Sticky Ratio), 2/1/0
Sepp 2014 Skewbeta, 2/1/0
Heuristic Sticky Regimes:
Sticky Local Vol
Sticky Strike
Sticky Delta
据说在波动率交易中一千个人有一千个Delta，和以上这些信息也有关。因为隐含波动率对现货/远期F是依赖的。

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In the dynamic study of volatility smiles, the following information is closely related and interconnected:

Implied Vol is the path average of Local Vol.

The slope of the Implied Vol surface is half that of Local Vol.

ATM Implied Vol = ATM Local Vol.

The regression coefficient of ATM Implied Vol under Local Vol on Ln F is twice the slope of the Implied Vol surface, i.e., the Rule of Two.

Bergeomi 2009 SSR (Skew Sticky Ratio), 2/1/0
Sepp 2014 Skewbeta, 2/1/0
Heuristic Sticky Regimes:
Sticky Local Vol
Sticky Strike
Sticky Delta It is said that in volatility trading, a thousand people will have a thousand different Deltas, which is also related to the above information. This is because implied volatility depends on spot/forward F.

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In the nearly four-week-long conflict with Iran, the oil market is experiencing a classic case of "time-based pricing." The release of strategic reserves has delayed the impact but cannot eliminate the supply gap; disruptions to tanker transport and delayed production recovery are causing inventory pressure to accumulate into the future. Once the critical mid-April mark is passed, the price mechanism will shift from "buffered volatility" to "gap-driven repricing."

More importantly, the game structure itself is also changing. The conflict is no longer characterized by "escalation followed by deterioration..."

Oil prices are approaching a critical point; what will happen in mid-April?

关于Sticky Regimes的相关研究或者书籍
Hagan et al (2002)
Bergomi (2009)
Kamal and Gatheral (2010)
Sepp (2014)
Bergomi (2016) Chapter 9
Derman and Miller (2016) Chapter 18

Research or books related to Sticky Regimes:
Hagan et al (2002)
Bergomi (2009)
Kamal and Gatheral (2010)
Sepp (2014)
Bergomi (2016) Chapter 9
Derman and Miller (2016) Chapter 18