Choosing between annual and daily volatility for hedging

A stock's returns mean-revert. Measured on annual returns its volatility is $10\%$, but measured on daily returns (and then annualised) it is $20\%$. You have sold a European option and will delta-hedge it daily. Which volatility should you use?

$20\%$, the daily volatility. Hedging P&L comes from gamma times the realised squared moves between rebalances, so what you pay for is the volatility of the small moves you actually hedge through. Mean reversion makes long-horizon variance smaller, but that does not reduce the cost of daily re-hedging.