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A derivative security pays a cash amount c if the spot price of the underlying asset at maturity is between K1 and K2, where 0< K1 < K2 and expires worthless otherwise.

Q: how to construct this derivative security using plain vanilla call options?

Could anyone tell me how to construct this type of derivative security specifically and generally? Thanks!

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Buy a [K1, K1+w] call spread and sell a [K2, K2+w] call spread, where w is as small as possible. The amount of notional of these you will need is c/w. The limit of this as w goes to zero is the payoff you desire. In practice you will be limited to whatever strikes are available to trade.

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