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The pnl for a teeny tiny move in spot is delta * spot_move + vega * vol_move (ignoring gamma, theta etc) which tells you that for the change in vol to offset the spot movement, the vol needs to move by -delta*spot_move/vega.
Here's what that looks like for a +$1 move in spot, at different strikes. At the 80 strike, the vol needs to drop by 1.2% to offset the gain from the spot movepic.twitter.com/wXDgpHL2Uk
(Actually its a bit more than this because I ignored gamma but w/e)
The vol surface is pretty flat around the 80 strike so skew is not really playing a role here (for an ATM option there would be a skew effect, where IV mechanically drops as spot increases, because you roll up the vol surface in strike space)
BUT the negative skew (puts > calls) implies a negative relationship between price and vol, i.e. all else equal you expect vol to drop when price rises, just like with stocks. So a 1.2% vol drop on a $1 price rise is not crazy at all
Hence the question -- if I buy OTM calls and spot moves up $2, how much money have I lost? :)
That's it for this round of #learninginpublic, now @volmagorov can explain all the ways I screwed it up.
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