In a BS world (constant volatility, no transaction costs, continuous hedging) If I buy or sell an option and continuously delta-hedge, I know how to calculate the final expected PnL based on implied vs realized volatility, but how do I calculate the PnL at some point in time before expiry of the option?
For example, I buy a 20dte call option at 24% IV and delta-hedge continuously. Realized volatility is 27% (and constant). How would I calculate the expected profit in, say, 8 days time?