Exactly. You're talking about a variance swap.Quote from gkishot:
They are index variance swaps contracts on CBOE.
The challenge is, no market can exist for a contract unless the exchange can convince sellers that they can effectively duplicate/hedge the contract using other assets. You can't make this work with speculators on both sides.
Index variance swaps *can* be duplicated/hedged using strips of underlying options, re-weighted as the underlying moves.
But when you're talking about random stocks, yes it can be done, but with relatively few option strikes (sometimes spaced apart 10-20% in value)... the costs will be very high. I'd expect a huge ask/bid spread for any individual stock.