Question 1 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, d 1 d 1 ​ , 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, at 10 am, March 8, 2019.