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Suppose a put option follows prices according the the binomial tree I've made and posted below and consider writing a put ($S$ is the stock value, $P$ is the put value, obviously). I want to find the portfolios (in periods 1 and 2) required to replicate the short put position assuming the stock increases in price during the first period and decreases during the second.

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My attempt:

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I believe I've done it correctly but I'm not sure if this is what it means to have a short put position. The jargon constantly throws me for a loop.

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