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 (