4. Assume the Black-Scholes framework For a certain stock, you are given: The current stock price is S The stock does not pay dividends The current volatility of the stock price is . The continuously compounded annual risk-free interest rate is r For European style call options on one share of the stock you are given: Delta 0.56 Gamma 0.10 Vega 0.08 Option X Option YTLR0.620.05 Option Z 0.66 0.03 0.21 You sell 100 of Option X You delta-gamma-vega hedge your portfolio using the stock and Options Y and z Calculate the number of each option and shares of stock you have in your portfolio. Show all work a. Number of Option X. 100 b. Number of Option Y c. Number of Option 2z d. Number of shares of stock (specify long or short) 4. Assume the Black-Scholes framework For a certain stock, you are given: The current stock price is S The stock does not pay dividends The current volatility of the stock price is . The continuously compounded annual risk-free interest rate is r For European style call options on one share of the stock you are given: Delta 0.56 Gamma 0.10 Vega 0.08 Option X Option YTLR0.620.05 Option Z 0.66 0.03 0.21 You sell 100 of Option X You delta-gamma-vega hedge your portfolio using the stock and Options Y and z Calculate the number of each option and shares of stock you have in your portfolio. Show all work a. Number of Option X. 100 b. Number of Option Y c. Number of Option 2z d. Number of shares of stock (specify long or short)