Sorry had to sleep for a little (5 -6 am when I was typing yesterday).
Anyways an option is like a Binomial tree where you can expand (call) or sell (put) the business.
*Next part is absolutely useless for CFA, but food for thought.*
If you have an American option it means that you have more than one oportunity to expand your business. You can expand it at period 1, 2, 3. Had to do this for my undergrad MT. Bascially you first calculate the business without expansion. After that you go to period 3 and see what happens to the firm value if you excercised your “expand” (call) option. The difference in price would be the value of an option at period 3. You then use both the options. The difference between the value of 1 option and 2 option is the value of an option in period 2. The is equal to the difference between an American and an European option. Obviously it could be 0 and the option are worthless (out of the money).
The Black Scholes is basically makes the Binomial tree into a model with infinite branches (that’s why we use e^). From what I heard from my prof who went to Booth, in real life people will just use C++ to make an infinite period model. A lot more robust because they’re allowed to control and change variables in each of the infinite periods.
Also using an option is just increase the leverage for a stock. Let say you pay 3 dollar for a call at a strike of 15. If it’s less than 15 you have all of your capital -100% return. If it goes to 20 then your return would be 67% (5/3). If you just bough the stock at $15 and the stock dropped by a $1 your return would be 6.7% (-100% for option). If it were to increase to 20 your return is only 33%.
Also I think what you saw was an European option. They expire automatically and once it expires you just get the difference between strike place and stock price automatically. You don’t have to “use” it since it’s automated. Most of the option places I have seen don’t actually give you the stock, but instead just give you a difference in strike and the market price. Easier to manage for these websites, they don’t want to be the one liable to storing the stock and strike prices for it’s cusomter.
I hope you can see it from my POV. Not trying to go against at al (arguing with you in two treads). If I offended you in anyway water under the bridge man. WATER UNDER THE BRIDGE.