3. Current stock price of Chevron Corp (NYSE.CVX) is $100. You believe that stock price will not move much for the next three months given the recent oil prices and the outlook of the global economy. As a portfolio manager specialized in the oil industry, you would like to trade options. Call options with the maturity of three months for a share of stock are available as following. (30 points) Type Call Call Call Call Strike $95 $100 $105 $110 Price 12.11 10.96 8.89 6.35 Delta 0.65 0.64 0.58 0.47 Gamma 0.015 0.017 0.017 0.018 Assume Chevron will not pay dividends in the next three months. You would like to trade 100 butterfly spreads, meaning they are based on 100*100 shares of stocks. a) Please use available call options to construct a butterfly spread strategy, show the table of payoff and profit. At what stock price levels, you make profits? b) What is the delta and gamma of your unhedged butterfly spread portfolio? c) How would you make the portfolio delta-neutral by using the underlying stock? 3. Current stock price of Chevron Corp (NYSE.CVX) is $100. You believe that stock price will not move much for the next three months given the recent oil prices and the outlook of the global economy. As a portfolio manager specialized in the oil industry, you would like to trade options. Call options with the maturity of three months for a share of stock are available as following. (30 points) Type Call Call Call Call Strike $95 $100 $105 $110 Price 12.11 10.96 8.89 6.35 Delta 0.65 0.64 0.58 0.47 Gamma 0.015 0.017 0.017 0.018 Assume Chevron will not pay dividends in the next three months. You would like to trade 100 butterfly spreads, meaning they are based on 100*100 shares of stocks. a) Please use available call options to construct a butterfly spread strategy, show the table of payoff and profit. At what stock price levels, you make profits? b) What is the delta and gamma of your unhedged butterfly spread portfolio? c) How would you make the portfolio delta-neutral by using the underlying stock