Question: Consider the log-normal asset price model with S0 = $80, σ = 30%, and r = 6%. Construct
(a) a delta-gamma neutral portfolio and
(b) a delta-rho neutral portfolio to hedge a short position on 500 calls expiring after 90 days with strike price $80, taking as an additional component a call option expiring after 120 days with strike price $85. Find the changes in value of these portfolios after 5 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%.