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0

I don't think that it has a name on its own, but you can write $$(S_T - K + K)\,1_{S_T>K} = (S_T-K)_+ + K\,1_{S_T>K}$$ so it's a 1 call plus K binary calls. Binary are hard to hedge, the payoff looks like _|‾, going sharply from out-of-the-money to in-the-money. The delta changes fast and it's difficult to hedge the position. In practice, you give ...

3

This looks like a binary option. Following this wikipedia article it is called an "asset or nothing call". The pricing formula in the Black-Scholes world is $$S e^{-q T} \Phi(d_1),$$ where $S$ is the current spot price, $q$ is the dividend yield, $\Phi$ the cdf of a standard normal and $d_1$ is as usual in BS. To my knowledge such options are much less ...

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