Consider a one-period binomial pricing economy. There are two dates only, date 0 and 1. A risky stock has price of $100 at date 0, and its final price is either $120 (at State 1) or $80 (at State 2) at date 1. The risk-free rate over this period is 5%. A European put written on this stock with a strike of $100 expires on date 1. Also, assume the physical probability of State 1 is 0.6 and it is 0.4 at State 2.
(a) What is the put price at date 0, if the market is free of arbitrage opportunity?
(a) What is the price of call with the same exercise price?
(c) Instead, suppose the put option is traded at $13 at date 0. Call option on this stock is not available. Is there an arbitrage opportunity? If yes, please describe a COMPLETE arbitrage portfolio which uses ONE share of the stock.