I need assistance on these four questions, please. The only information given is the first questions' details as it also gives the instructions and hints for the other questions below. Please help. Thank you.
Suppose you are a portfolio manager and you are going to use derivatives to construct certain portfolio. The current stock price for AAPL is $171.01 per share, at 10 am, March 8, 2019. You want to sell 1 unit of European Call on AAPL, with strike of $180 and maturity of 1 year. Suppose the annualized interest rate is 3%, the annualized drift for AAPL is 5%, no dividend, and the annualized volatility is 10%. In order to hedge the potential risk of your option, you are going to calculate several Greeks based on Black-Merton-Scholes model. Instructions and Hints: (i) In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001 . (It is understandable that calculation normal PDF and CDF can have computational error, so a quite wide range of answers is admitted.) (ii) You should carefully keep your intermediate calculation results, for example, d1, as they will be helpful for later questions in this assignment. (iii) You can use online Normal CDF calculators but NO BMS-Calculator (option price or Greeks calculator) is allowed. Since there will be lots of formula-oriented questions, it will be helpful to make your OWN program in Excel, Python, Matlab etc., in order to do calculation. Part 1: Greeks based on Black-Merton-Scholes Greeks Calculate the Call option price, Delta, Gamma, Vega, and Theta, at 10 am, March 8, 2019. After selling the option, you want to do Delta-Hedge immediately. So you are currently buying Delta shares of AAPL, where Delta is your calculation result in Question 1. Calculate the value of your portfolio (i.e. the net cashflow) of selling one unit of call, and buying Delta shares of AAPL, at 10 am, March 8,2019 . For example, if you construct your portfolio by borrowing $10, then the answer is -10 . Same for following questions. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001 . Suppose you are doing a monthly Delta-Hedge, that is, you re-hedge per month. After one month, at 10 am, April 8 , 2019, the stock price is $180.2, and you want to re-hedge right now. Calculate the additional amount of shares of AAPL you should buy (positive for buying, negative for selling) at 10 am, April 8, 2019, in order to rehedge. Think about why you are selling or buying stocks when the stock price goes up from the meaning of Delta Hedging. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001 . Enter answer here Calculate the change of your portfolio value (i.e. the net cashflow). Note that your answer should be in $ with new portfolio value minus previous value, in present value at 10am, April 8, 2019. in your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001
