There are three states of nature, A, B, and C and no inflation. We observe the following asset prices. The risk-free real rate is 2%. A stock with no dividend yield, its price goes up either 15%, or 2% or -10%. A European call option with strike price equal to spot price (stock price right now) is sold for 7% of spot price of stock.
(a) Draw the payoff trees of each assets.
(b) What are the risk neutral probabilities that are consistent with these asset prices?
(c) Price a European put option with strike price equals to spot price.