Question 2

Question2: Google is listed S = 2000, with one-month (1' = T t = 1) options as below. Suppose that r = 2% (C. C), and that G = 30% per year, and consider the following options portfolio: Number of shares (minus sign indicates option written) Strike price Calls Puts 1950 300 200 2000 400 375 2150 0 350 3) Find the net delta, gamma, and vega exposures of the portfolio? b) How many shares must be traded to achieve a delta-neutral position? What is the value of those shares? c) What will happen to the value of the options portfolio if the stock price immediately increases to 2050? What happens to the value of the shares you found in part (b)? What is the net gainfloss on the delta-hedged position? d) Now suppose that the portfolio owner decides to make the portfolio both delta and gamma neutral by modifying the number of shares as well as the number of 1200- 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? e) What will be the change in the value of the portfolio in (d) if the stock price increases immediately from 2000 to 2100? Compare this change to your answer in (c) for the portfolio that was only deltahedged. f) Repeat (e) for a stock price decrease from 2000 to 1900. g) Use my excel file \"Gamma-hedge" to simulate your results