I’ll throw in a few:
1. Put-call parity mnemonic
COX = POSO
i.e. Call at time 0 + bond face X = Put at time 0 + underlying
For European options, divide X by (1+i)^t
Replace 0 with t for all future durations
Shuffle terms in equation to derive synthetic positions and signs show whether long or short, e.g. C = P + S - X means long call has same payoff as combo of long put, long underlying, and short bond
2. Use the basic put/call diagrams to map out the more complicated strategies
E.g. long butterfly
Start from left hand side, the line segments from 0 to X1 and just before X2 form a simple long call @ X1. If I’m short 1 call @ X2, the payoff turns into a horizontal line to the right of X2; I short a SECOND call @X2, the payoff now slopes down and to the right. When I hit X3, I need a long call at X3 to get back to a horizontal line. End result: long 1 call @ X1, short 2 calls @ X2, long 1 call @x3
Now start from the right hand side. The line segments from infinity to X3 and just before X2 form a simple long put @X3. If I’m short 1 put @X2, the payoff turns into a horizontal line to the left of X2; I short a SECOND put @X2, the payoff now slopes down and to the left. When I hit X1, I need a long put @X1 to get back to a horizontal line. End result: long 1 put @X1, short 2 puts @X2 , long 1 put @X3
3. For any option strategy, to go from long to short (and vice versa), put a hypothetical mirror along the y-axis of the payoff graph and reflect the image.
I hope this helps!