Question

Consider a call option with a strike price of $60 where the underlying stock is currently trading at $67 the continuously compounded risk free rate is 5%, and the standard deviation of the stock returns is 40% per year. The option has 9 months to expiration. Using the Black-Scholes model, what is the value of the call option?

Answer 1

Solution.>

The Price of the Call option is $13.94

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

Type of Option	Call Option
Stock Price (S0)	$          67.00
Exercise (Strike) Price (K)	$          60.00
Time to Maturity (in years) (t)	0.75
Annual Risk Free Rate (r)	5.00%
Annualized Volatility (σ)	40.00%
Option Price	$          13.94	=S0*N(D1)-K*e-rt*N(D2)
Additional Calculation Parameters
ln(S0/K)	0.110
(r+σ2/2)t	0.098
σ√t	0.346
d1	0.600	=(ln(S0/K)+(r+σ2/2)t)/σ√t
d2	0.254	=D1-σ√t
N(d1)	0.726	=NORM.S.DIST(d1)
N(d2)	0.600	=NORM.S.DIST(d2)
N(-d1)	0.274	=NORM.S.DIST(-d1)
N(-d2)	0.400	=NORM.S.DIST(-d2)
e-rt	0.96319

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