1. Amazon is listed S = 2,950, with one-month (t = T - t = 1) options as below. Suppose that r= 1% (C. C.), and that o = 30% per year, and consider the following options portfolio: Number of shares (minus sign indicates option written) Strike price Calls Puts 2750 +400 -300 2950 +500 +300 3100 +50 -150 a) Find the net delta, gamma, and vega exposures of the portfolio? b) How many shares must be traded (long or short?) to achieve a delta-neutral position? What would be the cost of those shares? c) What will happen to the value of the options portfolio if immediately after you delta- hedge your portfolio the stock increases to 3,000? What happens to the value of the shares sold in part (b)? What is the net gain/loss on the delta-hedged position? d) Now suppose that the owner of the portfolio decides to make the portfolio both delta and gamma neutral by modifying the number of shares as well as the number of 2,950-strike price call options in the portfolio. How many of these calls should be bought or sold to achieve a gamma-neutral position? What is the new value for the number of shares that should be bought or sold for delta-neutrality? 1. Amazon is listed S = 2,950, with one-month (t = T - t = 1) options as below. Suppose that r= 1% (C. C.), and that o = 30% per year, and consider the following options portfolio: Number of shares (minus sign indicates option written) Strike price Calls Puts 2750 +400 -300 2950 +500 +300 3100 +50 -150 a) Find the net delta, gamma, and vega exposures of the portfolio? b) How many shares must be traded (long or short?) to achieve a delta-neutral position? What would be the cost of those shares? c) What will happen to the value of the options portfolio if immediately after you delta- hedge your portfolio the stock increases to 3,000? What happens to the value of the shares sold in part (b)? What is the net gain/loss on the delta-hedged position? d) Now suppose that the owner of the portfolio decides to make the portfolio both delta and gamma neutral by modifying the number of shares as well as the number of 2,950-strike price call options in the portfolio. How many of these calls should be bought or sold to achieve a gamma-neutral position? What is the new value for the number of shares that should be bought or sold for delta-neutrality