Question

Use Black-Scholes formula to find the price of 1-year call option with strike price of X=$110 if the current stock price is S=100, the standard deviation of annual stock return is 16.9014%, and risk-free interest rate is 7%. You may want to use Excel to do you calculations. Note that Excel function NORM.S.DIST(x,TRUE) is the cumulative distribution function of x for standard Normal (i.e., with mean 0 and standard deviation of 1) distribution.

Answer 1

Solution-

The table showing important parameters is-

Type of Option	Call Option
Stock Price (S0)	$       100.00
Exercise (Strike) Price (K)	$       110.00
Time to Maturity (in years) (t)	1.00
Annual Risk Free Rate (r)	7.00%
Annualized Volatility (σ)	16.90%

Now, we compute different parameters to use black scholes formula and its components (In Excel) as follows -

ln(S0/K)	(0.095)
(r+σ2/2)t	0.084
σ√t	0.169
d1	(0.065)
d2	(0.234)
N(d1)	0.474
N(d2)	0.407
N(-d1)	0.526
N(-d2)	0.593
e-rt	0.93239

Putting these in formula gives us-

Option Price

$           5.62

Answer

Thanks!

Sheet showing formula is also attached below for your reference-

Type of Option	Call Option
Stock Price (S0)	100
Exercise (Strike) Price (K)	110
Time to Maturity (in years) (t)	1
Annual Risk Free Rate (r)	0.07
Annualized Volatility (σ)	0.169014
Option Price	=IFERROR(IF(C4='--> Additional Info'!A3,C5*C18-C6*C22*C19,IF(C4='--> Additional Info'!A4,C6*C22*C21-C5*C20,"na")),"na")
Additional Calculation Parameters
ln(S0/K)	=IFERROR(LN(C5/C6),"na")
(r+σ2/2)t	=(C8+(C9^2)/2)*C7
σ√t	=C9*SQRT(C7)
d1	=IFERROR((C13+C14)/C15,"na")
d2	=IFERROR(C16-C15,"na")
N(d1)	=IFERROR(NORM.S.DIST(C16,TRUE),"na")
N(d2)	=IFERROR(NORM.S.DIST(C17,TRUE),"na")
N(-d1)	=IFERROR(NORM.S.DIST(-C16,TRUE),"na")
N(-d2)	=IFERROR(NORM.S.DIST(-C17,TRUE),"na")
e-rt	=EXP(-C8*C7)