Question

Consider the BS model with S0=120,μ=0.2,r=0.04,T=1 and σ=0.3. The price of a call option with strike price K=100 is

Answer 1

S' = Stock price =	120
D = Dividend yield =	20.00%
S = Stock price ajusted = S'*exp(D*t) =	98.2476904
K = Strike price =	100
r = rate =	4%
e = exponential value = exp(.) =	2.71828183
t = time =	1
s = standard deviation or volatility =	30%
* 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(98.2476904/((100*EXP(-4%*1))))+0.5*30%^2*1)/(30%*1^0.5)                                                                                

d1 =       0.224405            Hence, N(d1) = 0.5887790                       

.                                                                                    

d2 = d1 - (s*t^0.5)                                                                                  

=0.224405-(30%*1^0.5)                                                                       

d2 =       -0.075595           Hence, N(d2) = 0.469871                          

.                                                                                    

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

C =98.2476904*0.5887790-100*exp(-4%*1)*0.469871                                                                          

C = 12.701                                                                   

Price of call option = $12.701