4. Assume that you are a portfolio manager currently holding 10,000 shares of UPS common stock. You are concerned over the possibility of a significant decline in the price of the stock over the next few months and are considering various option hedging strategies. Assume that the stock has a volatility (standard deviation) of returns of 35% (the actual is currently around 28% ), that the risk-free interest rate is 3.00%, and that no ex-dividend dates are expected to occur in the interim. a. For the Jan 2023175.00 options (expiration 1/20/2023), compute, by both the long hand method (using a spreadsheet or calculator is fine) and by using your software, the theoretical Black-Scholes option value for: (i) the call (ii) the put (When solving by long hand, you must keep repeating until your answer is within $.01 of the Option! software computed price.) b. Compare your theoretical computed values with the reported actual call and put prices (bid-ask quote if available) and state whether each option is over or underpriced. c. How many options would you buy or write to establish an initial hedge on your 10,000 share position, that is, to make the overall position delta neutral? In other words: (i) Compute the hedge position using the calls. (ii) Repeat, but compute the hedge position using instead the puts. 4. Assume that you are a portfolio manager currently holding 10,000 shares of UPS common stock. You are concerned over the possibility of a significant decline in the price of the stock over the next few months and are considering various option hedging strategies. Assume that the stock has a volatility (standard deviation) of returns of 35% (the actual is currently around 28% ), that the risk-free interest rate is 3.00%, and that no ex-dividend dates are expected to occur in the interim. a. For the Jan 2023175.00 options (expiration 1/20/2023), compute, by both the long hand method (using a spreadsheet or calculator is fine) and by using your software, the theoretical Black-Scholes option value for: (i) the call (ii) the put (When solving by long hand, you must keep repeating until your answer is within $.01 of the Option! software computed price.) b. Compare your theoretical computed values with the reported actual call and put prices (bid-ask quote if available) and state whether each option is over or underpriced. c. How many options would you buy or write to establish an initial hedge on your 10,000 share position, that is, to make the overall position delta neutral? In other words: (i) Compute the hedge position using the calls. (ii) Repeat, but compute the hedge position using instead the puts