Question: 1. (20 marks) Consider a one-period model with 2 states and 2 assets: a bond and a stock. Assume that r = 0) so that

1. (20 marks) Consider a one-period model with 2 states and

1. (20 marks) 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. (1). Is this model arbitrage free? If yes, find a state price vector and a risk neutral probability measure. Is it complete? (2). 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 (as we did in class). 1. (20 marks) 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. (1). Is this model arbitrage free? If yes, find a state price vector and a risk neutral probability measure. Is it complete? (2). 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 (as we did in class)

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