Assume that I long ATM Call option on a stock at 20% implied volatility. This Call option will expire in 1 month. If, over this coming month, the underlying moves with 30% volatility and I delta-hedge this option. I expect to get profit from Gamma scalping. My expected P&L would be positive.
How would my P&L accumulate, on average,
Does P&L grow linearly over time, or does P&L grow exponentially over time?
Does moneyness of option affect accumulated P&L shape?