Assume Amazon stock pays no dividends during the next 3 months. Consider an option on Amazon stock which matures in three months time (assume 3 months is 0.25 years). The Amazon stock price is $61, the exercise price (i.e. strike price) is $60, the risk-free interest rate (continuously compounded) is 3% per annum and the volatility is 32% per annum. a. What is the price of the option if it is a European call? b. What is the price of the option if it is an American call? c. What is the price of the option if it is a European put? d. Verify that putcall parity holds. e. Suppose that today you write one million European call options on Amazon stock (meaning the buyer has the option to buy one million Amazon shares), what is the position that you take today to delta-hedge this option (you need to say whether you go long or short Amazon stock and how many shares (to the nearest 10 shares)). In parts (a), (b) and (c), give your answers in dollars correct to four (repeat 4) decimal places. As an intermediate step in your calculations, show the d_1, d_2, N(d_1) and N(d_2) terms which appear in the Black-Scholes-Merton formulae (a screen-shot of your excel spreadsheet inserted into your word document or PDF is more than adequate but you should make sure all answers appear to 4 decimal places).

you will need to use the NORMDIST or NORMSDIST functions built into excel.