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Consider a one-period model with 2 states and 2 assets: a bond and a stock. Assume that r= 0 so that the bond sells for $1 at t=0 and paid $1 at t=1. The initial stock price is $20 and it has two possible prices $30 and $15 at t=1.
a) Is this model arbitrage free? If yes find a state price vector and a risk neutral probability measure. Is it complete?
b) Find the prices of the European call and put options on the stock with strike price K=$20. Also find the replicating trading strategies which replicate the cash flows for the options at t=1.
Assuming that there are no storage costs, what is the value of the contract the investor holds after two months?
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