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Consider the log-normal asset price model with S0 = $80, sigma = 30%, and r = 6%. Construct (a) a delta-gamma neutral portfolio anti (b) a delta-rho neutral portfolio to hedge a short position on 500 calls expiring after 90 clays with strike price $80. taking as an additional component a call option expiring after 120 days with strike price S85. Find the changes in value of these Portfolios after S days if one of the following three scenarios will happen: (i) the stock drops to $75; (ii) the interest rate jumps to 9%; (iii) the stock drops to $75 and the interest rate jumps to 9.