Interest rates are 0. A stock is priced at $4. In each period the stock can double or half in price. Consider a two-period call option with strike of $3.

Below is the lattice of stock prices and European option prices in red.

(a) Use the above lattice of option prices to price a one-period compound option, that allows the holder to buy the call option for $1.00 in period one.

(b)Compute the price of a claim that at date 0 pays out the stock price squared after 1 period.