The crucial mistake you're making here is the fact that you think in invested dollars.Let me clarify:
Is there ever a situation where buying DEEP OTM calls will make you more money than buying ATM or ITM calls for the same amount of money invested?
In other words if a stock is $3, and you buy $100 worth of $3 calls (let's say this gets you 1 call), will this ever be worth less than if you buy $100 worth of $20 calls (let's say this gets you 60 calls)?
If price rockets up to $1,000,000 per share, will the ATM calls constantly be worth more than the OTM calls?
What I'm trying to uncover is, if you have enough money to buy even one ITM call, and you're long term bullish, will this during every case be a better play than buying a lot of OTM calls, even though you're getting more calls?
Every simulation I have run on this (using ToS) seems to be that the answer is yes (ITM/ATM always better), but I want to ask you.
Are DEEP OTM calls just for people with a little money to play around with?
The crucial mistake you're making here is the fact that you think in invested dollars.
"Am I better off investing 100$ into ATM or ITM or is it better to invest 100$ into OTMs?"
You cannot do that. Simply put if the stock rallies to 100$, you're way better if you invested into OTMs vs ATM or ITM, just because you have more options. 60x80 is more than 1x97...makes sense?
The question you have to ask yourself: Where do I think the stock will end up at before my options expire. You'll have a lot of busted OTMs but when you hit, you'll strike big. With ATMs you'll have less expired options but you won't make as much.
There is a reason why options are priced off of a return distribution which in turn can be modulated to probability of strike touch or expiration in the money.
If you are long term bullish, the best thing you can do is collaring your stock, meaning you sell a call and invest the premium into a downside put. This will reduce your P/L volatility by a significant amount so you can leverage more.
This, however, depends a lot on how good you are with options, so I suggest you invest some time into understanding the basics.
IMHO it was never a good idea to buy outright options unless you have a view on volatility. Options are always priced with a premium to realized vol so you'll always overpay unless you spread of your risk.
So, I am using ToS. Is their computation algorithm mistaken?now I can visualize MrMuppet hopelessly shaking his head..
OP, in your chart you are just visualizing a terminal distribution, but by doing so you are leaving out implied volatility and time decay. In reality the payoff won't be that linear.
Because you don't bet on the stock here, you bet on the implied vol of the LEAP.Yeah, I think in invested dollars. I want to spend the least and make the most.
Can you detail this? Collaring a stock? Say I have a big SNDL position. I do. I'm very bullish. I am. Why would I invest premium and buy puts if I'm bullish?