Say I buy a call option today, and I short the underlying stock with the delta.
What is the value of this portfolio today?
Then, one period later, say there's a change in the stock price. That also changes the Delta. So, say I go out and adjust my portfolio, so I am still delta short in the underlying.
What is the value of this portfolio today?
What is my PnL over this period?
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.
Delta hedging determines the adjustments that you make to your position. It has nothing to do with the value of your individual positions.
P&L is determined by calculating the difference between the opening cost of each position and today's value of each position and then summing up all of the gains and losses.
