If the cheap option is a means of paying for data, then it could be considered a "free" lottery ticket. Any returns on that option are simply a bonus. If I was doing this, I would be looking for a 1c or less option as close to the money as possible and with only a few days (or less) until it expires. This is when close out-of-the-money options become very cheap and yet have the best opportunity of making something
IF the underlying makes a big move into expiry in the direction of your option. No guarantees - but it can and does happen on rare occasions. Risk to reward is great as you are paying the money for data anyway - and even if you only had a win once a year on the option, it's a bonus.
If you buy something further out in time for 1c, the market really would have to make an extraordinary to make anything on it.
Not recommending this as a strategy in itself as time is working heavily against such a position. But it is the greek component in option pricing called "gamma" that can make that option accelerate rapidly as expiry approaches and if the share price exceeds your option strike price - otherwise known as being "in-the-money".
I sometimes use a version of this strategy to hedge gamma in front month short options coming into expiry. In fact, this is the type of trading I would have been doing with IB if the account was still open. While the strategy mostly loses and the options expire worthless, it can provide cheap gamma insurance coming into expiry.
My
- hope this helps!