3. 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 re-hedge.

4. Calculate the change of your portfolio value. Note that your answer should be in $ with new portfolio value minus previous value, in present value at 10 am, April 8, 2019.

5. Back to at 10 am, March 8, 2019. Suppose you are constructing another portfolio by buying a European Call on AAPL with strike 180 and selling the European Call on AAPL with strike 185.Without volatility skew, that is, volatility is always 10% for different strikes. Calculate your portfolio value V, at 10 am, March 8, 2019.

6. Now you are focusing on portfolios with digital options on AAPL, at 10 am, March 8, 2019. All the information about the stock stays the same, and we are back to a world of constant volatility 10% again.Note that the payoff of this option at maturity is: 1STK . Calculate the price of digital call option on AAPL with strike 180 and maturity of 1 year, at 10 am, March 8, 2019.

Think about the proper range for the digital option's price, from the Put-Call Parity. In addition, compare this number with the Delta of European Call in Question 2, think about why.

7. Suppose you are going to sell this digital option at the price you calculated at Question 11 now. Meantime, you want to do Delta-Hedging to lowered potential risk. Calculate the amount of shares of AAPL you should buy or sell (positive for buying, negative for selling), based on Black-Scholes model, at 10 am, March 8, 2019.Again, compare this number with the Gamma of European Call in Question 3, think about why?

8. Suppose you are constructing another portfolio by buying a digital European Call on AAPL with strike 180 and selling a digital European Call on AAPL with strike 185.Calculate your portfolio value W , at 10 am, March 8, 2019.

Please help me in question no. 3,4,5,6,7,8