Question

Current market price:                                          $95

Strike/exercise price:                                           $100

Risk-free rate (r_f):                                                     5%

Time (in years):                                                         .25

Standard deviation:                                              25%

The standard deviation is the risk associate with an option.  The greater the standard deviation, the greater the risk of an option.

Use the Black-Scholes Option Pricing Model and calculate the price of this option.

Answer 1

S=95

K=100

t=0.25

r=5%

sigma is 0.25

d1=(ln(95/100)+(5%+0.25^2/2)*0.25)/(0.25*sqrt(0.25))=-0.2478

d2=(ln(95/100)+(5%-0.25^2/2)*0.25)/(0.25*sqrt(0.25))=-0.3728

N(d1)=0.4021
N(d2)=0.3546314

Call option price C=95*0.4021-100*e^(-5%*0.25)*0.3546314=3.1794

Put option price P=C+Xe^(-rt)-S=3.1794+100*e^(-5%*0.25)-95=6.9372