There are three states, A, B, and C and no inflation. We observe the following asset prices. The risk-free rate is 2%. A stock has no dividend yield; its price goes up either 15%, or 2% or -10% in each state, respectively. An European call option on stock with a strike price that is equal to the current spot price of the stock is sold with a price that is equal to 7% of current stock price.

(a) (3 points) Draw the payoff tree for each assets.

(b) (4 points) What are the risk neutral probabilities that are consistent with these asset prices?

(c) (3 points) Draw the payoff tree of a one-period European put option with a strike price that equals the current spot price of the stock. Price it as a percentage of current stock price.

(d) (bonus 5 points, hard) Draw the payoff tree of a two-period European call option with a strike price that equals the current spot price of this stock. Price this asset, also as a percentage of current stock price.