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I'm studying for a test and am stuck on this practice question:

With interest rates equal to 0, two different stocks $S_1$ and $S_2$, both valued at \$1 today, can be worth \$2 or \$0.50 at some point in the future. If the option that pays \$1 when both $S_1 = S_2 = \$2$ is traded in the market and is worth \$0.125, calculate the price and replicating portfolio of the option that pays \$1 when $S_1 = \$2$ but $S_2 = \$0.5$. You may leave your answer in matricial form.

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1 Answer 1

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Hint The future world has 4 states: $(0.5,0.5), (2,0.5), (0.5,2), (2,2)$. You have 4 instruments - cash, each stock, and an option they are both \$2 which is traded. Take $x,y,z,w$ of each and match the portfolio to the price of the option in each market state.

You get 4 equations and 4 unknowns, solve, and supposedly you get a unique solution, which immediately yields the replicating portfolio.

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Got it. Didn't think to use the given option as the 4th instrument. Thanks! –  user108 Feb 25 at 14:34

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