Why perfect delta-hedging still leaves random P&L
Asked at Jane Street, SIG
You sell an option, price it at exactly the volatility the stock will realize, and delta-hedge it, but only at discrete moments (say once a day), not continuously.
Even with the "correct" volatility, your hedging P&L is random. Where does the noise come from, and how does it shrink as you hedge more often?
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.