2. (Options) Consider a world with two stocks (S, and S) and two possible states. The stocks can be purchased in period t. In the first state, which happens with probability 0.5 the stocks can be sold in t + 1 for 20 and 10 dollars respectively. In state 2, the stocks can be sold in t+1 for 5 and 25 respectively. i) What combination of assets will secure a selling price int+ 1 for the portfolio of 15? ii) What option type and strike price) can be underwritten on the first stock in order to secure this same selling price in t+1? For the rest of this question the interest rate between periost and t + 1 is 5% iii) What is the price (option premium) of the option in the previous part? What is its intrinsic value? (Hint: What is the expected discounted gain from having the option? Notice that the option will only be exercised in t + 1 if one of the two states of the world is realized.)