We prove that the skew stickiness ratio converges to two at short maturity under local volatility models.  This appears to be the first rigorous proof of this limit for a general time-dependent local volatility function.  As a by-product, we strengthen the one-half rule of the implied volatility skew by removing uniform ellipticity and global bounds on spatial derivatives of order at least two.  The proof uses a first-order Watanabe expansion.

Zoom Meeting link:  texastech.zoom.us/j/3067000354

Meeting ID:  306 700 0354

Passcode:      TTUMF