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Problem 284 of 333MediumLinear AlgebraP284
State prices from three traded assets
A stock trades at 100 today. In one period it ends at 80, 100 or 125. Three assets trade:
- a bond paying 1 in every state, priced at 0.95
- the stock, priced at 100
- a call on the stock with strike 100, priced at 8
(a) Find the price of each Arrow-Debreu security (pays 1 in one state and 0 in the other two) by replicating it with the three assets.
(b) Is there an arbitrage? Keeping the bond and stock prices fixed, for which call prices would there be one?
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