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, nd 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 nd the

replicating trading strategies which replicate the cash

ows for the options at t = 1 (as we did in class).