Question

what is the value of a european call option with an exercise price of $40 and a maturity date six months from now if the stock price is $28 the instantaneous variance of the stock price is 0.5 and the risk free rate is 6% use both a) two step binomial tree b) black scholes pricing formula

Answer 1

Solution.>

Using two-period Binomial formula:

The price of the European Call option is $3.06

I have solved this question in Excel. The formula used are shown in another excel file. If you still have any doubt, kindly ask in the comment section.

The formula used are:

Using Black Scholes pricing formula:

The price of the call option is $2.50

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)	$          28.00
Exercise (Strike) Price (K)	$          40.00
Time to Maturity (in years) (t)	0.50
Annual Risk Free Rate (r)	6.00%
Annualized Volatility (σ)	70.71%
Option Price	$            2.50	=S0*N(D1)-K*e-rt*N(D2)
Additional Calculation Parameters
ln(S0/K)	(0.357)
(r+σ2/2)t	0.155
σ√t	0.500
d1	(0.403)	=(ln(S0/K)+(r+σ2/2)t)/σ√t
d2	(0.903)	=D1-σ√t
N(d1)	0.343	=NORM.S.DIST(d1)
N(d2)	0.183	=NORM.S.DIST(d2)
N(-d1)	0.657	=NORM.S.DIST(-d1)
N(-d2)	0.817	=NORM.S.DIST(-d2)
e-rt	0.97045

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