Question

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

1. In 6 months the price will be $2369.10. Assume the volatility of Amazon is 27% and the strike price is $2379.10, find out how much your option in part 1 costs by using the Black-Scholes formula.

Answer 1

Solution.>

The price of the call option is $175.51

The Call option price formula is: =S0*N(D1)-K*e-rt*N(D2)

I have solved this question in Excel. The formula used are written along with the values. If you still have any doubt, kindly ask in the comment section.

Type of Option	Call Option
Stock Price (S0)	$       2,367.92
Exercise (Strike) Price (K)	$       2,379.10
Time to Maturity (in years) (t)	0.50
Annual Risk Free Rate (r)	0.10%
Annualized Volatility (σ)	27.00%
Option Price	$          175.51	=S0*N(D1)-K*e-rt*N(D2)
Additional Calculation Parameters
ln(S0/K)	(0.005)
(r+σ2/2)t	0.019
σ√t	0.191
d1	0.073	=(ln(S0/K)+(r+σ2/2)t)/σ√t
d2	(0.118)	=D1-σ√t
N(d1)	0.529	=NORM.S.DIST(d1)
N(d2)	0.453	=NORM.S.DIST(d2)
N(-d1)	0.471	=NORM.S.DIST(-d1)
N(-d2)	0.547	=NORM.S.DIST(-d2)
e-rt	0.99950

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