{20 points} Let K1 {2 K2 denote strike prices and con- sider a portfolio P that consists a long position on one European put at strike price K2 and the short position on one European put at strike price K11 both puts nia- turing at time T. Both puts are written on a stock whose value at time T is denoted ST. (a) [5 points} What is the pavo muming zero costs for the putsj 'on'i the portfolio when K1 = 25, Kg = 35 and S]- = 30. (b) (5 points) What is the name of such a portfolio? What would be the expectation of the investor about the behavior of the stock? (c) [5 points} lGive explicit formulas, as a function of ST and the other data: for the total payoff of the portfolio (assuming zero cost for the puts) at time T. (d) {5 points} Graph the payo. (e) [5 points} Suppose now you take into account the pric p1 and pg of the puts. Which of these two is greater? Draw in your graph the prot from the portfolio in the case where 331 and pg are taken into account