ok so now think of a bull call spread: You buy a call with a low exercise price XL and sell a call with a high exercise price XH.
You should always ask for three questions while determining the formulas:
How much did you spend on the strategy? (Net Premium) (associate with maximum loss)
What did you expect from the strategy? (stock price ranges that won’t hurt you)
What should be the stock price that would help you recover your cost?
Let’s then decide what can be the maximum loss?
say none of the calls were in the money (which is usually the case here) and the stock price went to 0 so that nothing ended up being in the money. (most strategies have max loss = net premium)
You’ll lose all that went into your strategy. That is your net premium.(Cost of long option - cost of short option)
Now think of break even. You’d want to benefit only to the extent that whatever you spent must be recovered.
(what should be the stock price that would help recover the cost)
So the purchased option should finish in the money by an amount equal to cost of strategy.
XL + (net premium) or XL + (C0L - COh)
Now think of what did you expect from the strategy? Your intent was to gain from the long option and the short option was used to finance the long option but it will limit your upside by the high exercise price.
So the maximum you will gain is at the point where the second option will start being in the money. That point is the higher exercise price. So you start making money when you exceed the low exercise and reach the high exercise. Hence that band of money is XH-XL. Now this money making ability came at a cost = net premium,
so max profit = XH - XL - (net premium)
= XH - XL - (CoL - CoH) = XH - XL - CoL + CoH
I just hope i didn’t make any mistakes because didn’t review it before posting. I’d be embarassed if there’s a stupid mistake. But I guess this is correct. I hope this helps.