Quote from Strangler:
I'll save you some runaround and answer your question in basic terms.
"Is there a way to know how much that option would be worth if price droped to 45? Or 40? Or 38?"
What you are asking is called delta. Delta ranges from 0 to 1. If a stock has a delta of 1, that means if the stock moves up by $1, the option will move up/down by $1. A delta of 1 is rare and only applies to deep in the money options.
In your example your $3 option probably has a delta of 0.5 if it is at the money. So if SPY went from $40 to $39, your put would go up $0.50 to $3.50. However other factors will influence delta (ie time remaining, volatility, etc.) so it is not an exact science.
Many brokers will give you delta information but there's an easier way to get a quick estimation. If you wanna find out what would happen to your 40 put if SPY dropped by $2 tomorrow, just look at the current bid for the 42 put. If you wanna find out what would happen if SPY went up $3 tomorrow, look at the bid on the 37 put.