I am reading more on second derivatives and something is baffling me. Nearly every page that talks about vanna(really just a handful) all say calls and short puts have positive vanna and short calls and long puts have negative vanna. why is this? If I am long a call, yes I want the IV to keep going up to increase the value of the call. This makes sense. If I am short a put, I don't want IV's to go up, therefore shouldn't I want vanna to be negative?

Similarly, for gamma, long puts and calls are positive gamma. I don't understand why vanna is different.

Also, these articles don't distinguish between ITM and OTM. A call option that is ITM will have delta go up as IV goes down. 

I read Harley Bassman's paper on calls being underpriced and it seems intriguing. You can read the paper here: http://www.convexitymaven.com/images/Convexity_Maven_-_The_White_Swan.pdf

I did some digging on SPX options and pretty much see what he has been seeing. This image I am posting is of the jan 21, 2022 SPX options data. The thicker red vertical line was the price at the point I looked into the data. the 6 thinner red lines are -30%, -20%, -10%, +10%, +20%, +30% from the current price. The thicker colored slopes are IV's and the thinner colored slopes are option prices. It is a bit hard to see when you can't mouse over the values but the important part is that SPX 4700 (~20% from here) calls are at $36.9 and the equivalently priced puts are around the $2200 strike which is a ~43% drop from here. You can see that IV's are rich for puts and cheap on calls which is to be expected. I think if we melt up then there might be some major returns to be had here. IV's in calls have room to adjust to the upside. In july of last year this exact scenario played out.

I know there are a lot of bears here but I thought I would post this and see what others thought. There are two sides of a trade and more and more the inflation side seems to be the narrative.