A stock sells for 173 What is the price of a nine month call

A stock sells for 173. What is the price of a nine month call option at 170 if the interest rate is 4% and the standard deviation of the stock is 35^s

Solution

For European options:

S = Stock price =

173

K = Strike price =

170

r = rate =

4%

e = exponential value = exp(.) =

2.718282

t = time =

0.75

s = standard deviation or volatility =

35%

* N(d1) is Normal distribution probability value

* N(d2) is Normal distribution probability value

Use normal distribution table

d1 = (Ln(S/(K*exp(-r*t))+0.5*s^2*t)/(s*t^0.5)                                                                            

=(LN(173/((170*EXP(-0.04*0.75))))+0.5*0.35^2*0.75)/(0.35*0.75^0.5)                                                                          

d1 =       0.308241           

Hence, N(d1) = 0.621051                          

d2 = d1 - (s*t^0.5)                                                                                  

=0.308241-(0.35*0.75^0.5)                                                                                

d2 =       0.005132109     

Hence, N(d2) = 0.502047406                   

C = S*N(d1)-K*exp(-r*t)*N(d2)                                                                         

=173*0.621051-170*exp(-0.04*0.75)*0.502047                                                                        

C = 24.6161                                                  

Value of call option = $24.62