Blazin
Creative Title
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Yes at the money means the stock is trading at the strike price.
When a stock price moves the options move but this movement is not 1:1. THe delta is the ratio between those two movements. The delta is changing as well it represents at that moment. So in your example it would make no sense for delta to be larger further out of the money, the close they are to being in the money the more they will move in whole dollar terms. What you are thinking may make more sense if you think as a percentage. Assume a stock moves $1. A way out of the money option with a very small delta may go from 0.03 to 0.04 that's a one penny change for a $1 move but as a percentage it's quite large. An option very near the money during the same $1 move may go up $0.50 from $2.00->$2.50 a much smaller percentage change but a much larger dollar move.
Prices for options can be multiplied by 100 as 1 contract is the minimum. So if it's 0.25x100=$25 cost per contract.
The $145.25 comes into play because that is your break even. Yes the strike was $145 but you paid 0.25 for the option. You always combine the strike and the amount you pay to determine your break even.
Because of math. I give the range as I can't know the exact amount but based on the delta I can approximate how the option would price in the near term based on a give movement.
I apologize for the vanessa style post but probably most functional given the intent.
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