Problem 7.4.10. (Delta-, gamma-, and theta-hedge given option Greeks table) Assume the Black-Scholes framework. You are given: (i) The current price of a nondividend paying stock is 50. (ii) The stock's volatility is 30%. (iii) The continuously compounded risk-free interest rate is 8%. (iv) The following information about two European call options on the stock: Price Delta Gamma Theta (Per Year) Call A 10.0618 0.6951 0.0191 -4.1201 Call B 6.0214 0.5056 0.0217 -3.9835 In each of the following cases, calculate the amount of the net investment you make today (including the sale of the 1,000 options in the first place): (a) You have just sold 1,000 units of Call A. You immediately delta-hedge your position with shares of the stock. (b) You have just sold 1,000 units of Call A. You immediately delta-hedge and gamma-hedge your position with shares of the stock and Call B. (c) You are now further given that Call A is 50-strike and Call B is 60-strike, and both of them are 18-month call options. You have just sold 1,000 units of a 50-strike put oth- erwise identical to Call A. You immediately delta-hedge and theta-hedge your position with Call A and Call B. Problem 7.4.10. (Delta-, gamma-, and theta-hedge given option Greeks table) Assume the Black-Scholes framework. You are given: (i) The current price of a nondividend paying stock is 50. (ii) The stock's volatility is 30%. (iii) The continuously compounded risk-free interest rate is 8%. (iv) The following information about two European call options on the stock: Price Delta Gamma Theta (Per Year) Call A 10.0618 0.6951 0.0191 -4.1201 Call B 6.0214 0.5056 0.0217 -3.9835 In each of the following cases, calculate the amount of the net investment you make today (including the sale of the 1,000 options in the first place): (a) You have just sold 1,000 units of Call A. You immediately delta-hedge your position with shares of the stock. (b) You have just sold 1,000 units of Call A. You immediately delta-hedge and gamma-hedge your position with shares of the stock and Call B. (c) You are now further given that Call A is 50-strike and Call B is 60-strike, and both of them are 18-month call options. You have just sold 1,000 units of a 50-strike put oth- erwise identical to Call A. You immediately delta-hedge and theta-hedge your position with Call A and Call B