Question

Today, the continuous compound interest rate is 0.1% and one share of Amazon is $2367.92.

a. What price do you expect Amazon to be 6 months from now? What European style option should you buy in this case? Your future price can’t be a whole dollar, everyone should have different future stock price.

b. Assume the volatility of Amazon is 27% and you set your own strike price to 2 decimal places, find out how much your option in part 1 costs by using the Black-Scholes formula. You strike price can’t be a whole dollar, everyone should have different strike price.

Answer 1

1.

S0: Present share price = $2367.92

r: interest rate = 0.1%

time = 6 months = 0.5 years

s: standard deviation = 27%

z: is a random number between -1.96 to 1.96

Assume z = 1

e: natural exponent

St = 2367.92*e^(0.1%*0.5+1*27%*(0.5^0.5)) = $2880.41 (expected stock price after 6-months)

Since the expected stock price has increased, I will prefer to buy a European call option

2. K: strike price = 2870.41 (assumed)

So current stock price = 2367.91

r risk free rate = 0.1%

s: standard deviation = 27%

t: time to maturity = 6month = 0.5 year

d1 = -0.90993

d2 = -1.10085

N(d1) = normsdist(d1) = 0.1814

N(d2) = normsdist(d2) = 0.1355

C: value of call option

c = $40.92 (price of European call option)