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If I understand well, you have a market with 3 states: up, flat or down. You have 3 instruments: The stock The risk-free rate (50%) The option If you can create a portfolio today with these 3 instruments that can replicate de payoff of the option you have to price, then the law of one price tells you that the price of the option should be the price of ...


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The state price vector are the prices of securities which pay \$1 if and only if that state of the world occurs. This is just a question of being able to replicate the payoffs $$ \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}, \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} $$ with payoff vectors $\vec{b} = [1,1,1]^T$ and ...


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these kinds of questions usually require careful attention to details: if it's a hw question of some kind, consult shreve's lecture notes, he has a whole section on this precise topic in all its glory. as for intuition, since holding $\frac{\partial \xi}{\partial S}$ at any point in time eliminates the dW term, in the context of a discrete time period model ...



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