mmencke
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That is a good point. Maybe the underlying is assumed to be a futures contract?

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I think you are missing the initial value of the short position. If you set $K=S_t$ (buy at-the-money options) and short the stock at price $S_t=K$, then your payoff will be $2(x-K)^++(K-x)$, so $x-K$ if above $K$ and $K-x$ if below $K$.

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