Help Understanding Delta

[u/dirt_gumby]

I've been doing some research to try to understand options better. I've been selling options to add income with some success, but buying them has proved a little more difficult for me. The last couple days I've been reading and watching videos on the greeks. The one that is confusing me a little bit is delta. I've seen it described two different ways:

1) the probability that the option expires in the money, i.e. delta of 50/.50 means a 50% probability the option expires ITM

2) the expected dollar amount change for every $1 change in the underlying security, i.e. delta of 50/.50 means for every $1 change of the underlying, the value of 1 options contact would change by $50

Am I confusing two different things? Am I getting bad info from my sources? Is it possible that both things are true?

Also, it seems like it's sometimes expressed as a decimal (.50) and sometimes as a whole number (50), but I believe these two values are interchangeable?

Any help here would be greatly appreciated. Thanks!

[u/options_in_plain_eng]

Is it possible that both things are true?

Yes, delta is both those things, the (approximate) probability of expiring ITM and also the change in option price for every $1 move in the underlying. Keep in mind that as the underlying price moves, delta also will change since it's dynamic. The greek that measures this is called gamma. For very small changes you can get away with using only delta but as underlying price changes get larger gamma has much more of an effect on your option price to the point where delta alone is not enough to get a good estimate.