I have a question about delta and its relation with the long call option. If I plan to buy a long call option to bet the stock price will go up. Is larger delta value better or smaller delta value better in terms of profit gain? For example, a stock is at 100 dollars right now. I decide to buy a call option with an expiration date 6 months later. The option with strike price 110 dollars has delta 0.45 and the option with strike price 120 dollars has delta 0.40. So, which option is better? Moreover, if we also consider in the money options (options with strike price lower than 100 dollars), does the answer change? Thanks
You really need to model some numbers to get a big picture view of what the possibilities are. Here are some current bid quotes for IBM's 11/20 calls:
IBM = $120
120c = $5.60
125c = $3.35
130c = $2.00
135c = $1.00
Assume that you buy one call. What will the above calls be worth at expiration at $125, at $130, at $135 and so on?
Plan B: Pick an arbitrary amount, say $2,500. Buy as many of each call as you can with $2,500.
Again, what will these positions be worth at expiration at $125, at $130, at $135 and so on?
The above ignores delta.
Download an Excel spreadsheet for option pricing or get some pricing software or use your broker's option analytics and repeat the above exercises and then vary the time between now and expiration.
By now, you show be realizing that asking whether a 45 delta call is a better choice than a 40 delta call isn't going to help you understand the big picture.
If calls are out of the money, the "delta" gets closer and closer to zero as you get nearer expiration.
If calls are in the money, the "delta" gets closer and closer to one as you get nearer expiration.
Is larger or smaller delta value better in terms of profit?
Delta has nothing to do with profit.
You can have a high or low profit (or indeed high or low loss) with either a high or low delta.
Moreover, the delta would have changed (drastically) throughout the trade. Delta "when you first begin the trade", again, is sort of meaningless in terms of "how much profit will you make".
Say you asked: "how does the sell price affect profits?" ... the question is off-track. Sure, obviously a higher selling price "affects" profits but it's kind of a misguided question. (You can't - obviously - anyway know what the selling price will be when you enter.)
"Delta" is basically a tool to "help you think" about what you are doing while trading.
I easily found an article which nicely talks about "delta" article, perhaps it will help the OP.