What is left when you delta-hedge a short straddle?
Asked at Optiver, Jane Street
You sell an at-the-money straddle for \8$ and, unlike the naked case, you continuously trade the underlying to keep your net delta at zero until expiry.
With the directional exposure hedged away, what determines whether you make money? State the condition in terms of realized versus implied volatility.
Show a hint
If direction is neutralized, only the size of the moves matters. Two forces are left: the decay you collect and the losses from re-hedging.