Question

Assume that you have been given the following information on Purcell Industris: (Formula in Excel)
Current stock price =	$15.00		Strike price of option =	$15.00
Time of maturity of option =	6	months	Risk-free rate =	6%
Variance of stock return =	0.12
d1 =	0.24495		N(d1) =	0.59675
d2=	0		N(d2) =	0.5
Binomial Lattice of stock prices:
P=			P(u)=
Cu =			P(d) =
Cd=
πu =
πd
According to the Black-Scholes option pricing model, what is the option's value?
Current value of option
Vc=

Answer 1

The current value of the stock option with the use of Black-Scholes option pricing model is determined as below:

Option Value = SN(d1) - Ke^(-rt)*N(d2)

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Here, S = $15, N(d1) = 0.59675, K = $15, r = 6%, T = 6/12 = .5 and Nd(2) = .50000

Using these values in the above formula, we get,

Option Value = 15*0.59675 - (15*e^(-6%*.5))*.50000

With the use of Exponential Function (EXP) of EXCEL/Financial Calculator, we get,

Option Value = 15*0.59675 - 15*.970446*.50000 = $1.672905 or $1.67

Answer is $1.67

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Note:

How to calculate exponential value in EXCEL?

Open an EXCEL Sheet and type =exp in any cell. Put in the number in the brackets like as follows:

=exp(-6%*.5)

This function will result a value of .970446 which has been used in the above calculation.