In the book 'Dynamic Hedging', Nassim Taleb writes:
All operators in options learn that a rise in volatility would cause the delta of an out of the money call to rise and that of an in the money call to drop, thereby bringing deltas closer to 50%.
Why is this? Why would the OTM delta rise? It can only rise if the underlying rallies. But if underlying rallies, the ITM delta will also rise, approaching 1. Why would it drop?