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What's the formula for profits and losses when I delta hedge?
You don't mention any specific numbers, so I'll answer in generalities. Say I buy a call option today, and I short the underlying stock with the delta. The value will be the value of the option you bought less the value of the stock you are short. (your premium is not included in the value since it's a sunk cost, but is reflected in your profit/loss) So, say I go out and adjust my portfolio, so I am still delta short in the underlying. It's still the value of your options, less the value of the underlying you are short. What is my PnL over this period? The end value of your portfolio less what you paid for that value, namely the money you received shorting the underlyings less the premium you paid for the option.