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???? on what? Say some big cap gaps down 20% after the open. Assuming I had a hedge with ATM puts wouldn't I recoup much of that loss with what I gain on puts that are now in the money?

How sensitive are equity option prices to changes in prices in their underlyings (large cap stocks)? The reason I'm asking is b/c I was looking at some option quotes on CBOE.com for stocks that moved big time (say 25% or so on a given day) and barely anything changed in option chains! I was...