no, you can buy as many options as you want, or is in supply. If...

no, you can buy as many options as you want, or is in supply.
If you never choose to exercise them they simply expire into the abyss.

I didn’t check your math, but yes you have the right formulae if you were to do it.

Options can be a good option (lol) if you want to hold a large numbers of shares in the future, that you ordinarily couldn’t buy at the present point in time, because they are a 1-1 conversion. Generally this is because the price of options lags behind the share price relative to time. The closer the time gets to the expiry, the greater the price will parallel the share price. You can now exercise them in the future regardless of their SP value due to the fixed strike price when you have the funds available too.

Another factor to consider is their liquidity, they won’t always trade at the volume of the share price, if they are shit options or closer to expiry.

I personally don’t buy them because I’m lazy and can’t be f*ed exercising them, if I was to buy them I would 9/10 times be looking to exercise them.

hope this helps