Assume the Black-Scholes framework. You are given the following in- formation on two European calls written on the same non-dividend-paying stock, whose current price is 55. Option 0.5-year 55-strike call 1.5-year 57-strike call Delta 0.6051 0.6456 Gamma 0.03 0.01674 Theta -6.8494 -4.5091 The volatility of the stock is 33%, while the continuously compounded risk-free interest rate is 7%. You have just purchased 100 units of 0.5-year 55-strike call and you immediately hedge the position. (i) Suppose you delta-hedge by trading 1.5-year 57-strike puts (but not calls) and cash. The total value of the hedge portfolio is 0, which consists of 100 units of 0.5-year 55-strike call, N units of 1.5-year 57- strike puts and W amount of cash. Determine N and W. (ii) Suppose you delta-hedge and gamma-hedge by trading the underlying stock, 1.5-year 57-strike puts and cash. The total value of the hedge portfolio is 0, which consists of 100 units of 0.5-year 55-strike call, X units of 1.5-year 57-strike puts, Y shares of the underlying stock and Z amount of cash. Determine X, Y and Z