Problem 4 (Problems 2 $5 3 continued). Wherever needed, you can use a software to work with matrices and equations in this question. The threestate model in questions 2 85 3 can be completed by including an option as the third asset. Let this additional asset be a call option expiring at t = 1 with exercise price K = $15. Assume Z; denotes the value of this option, and suppose the market price of this call is Z0 = $6.25. (a) Write the payoff Voctor ZT. Write the 3 by 3 cash-ow matrix D , and the vector of initial prices so for the new economy. Show that detD 75 0. (This means Rk(D) = 3 and hence the added call option is not a redundant asset.) (b) Use the rst F TAP to show that the new economy is still arbitrage-free. (3 Consider the ut 0 tion Y dened in uestion 2. Find a ortfolio 57' = 6 61 52 that re heates the P P P P payoff of this put. Here, 5"] is the initial amount of cash invested in the bank account, 51 is the number of stock shares at t = U, and 52 is the number of call Options (Z) at t = D. What is the no-arbitrage price of the put option Y