Consider a 1year option with exercise price 85 on a stock wi

Consider a 1-year option with exercise price $85 on a stock with annual standard deviation 10%. The T-bill rate is 2% per year. Find N(d₁) for stock prices $80, $85, and $90. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Solution

S

N(d1)

$80

0.3608

$85

0.5987

$90

0.7943

Notations:

S = Stock price

K = Strike price

r = rate

e = exponential value = exp(.)

t = time

s = standard deviation or volatility

* N(d1) is Normal distribution probability value for calculated d1

1.

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

=(LN(80/((85*EXP(-0.02*1))))+0.5*0.1^2*1)/(0.1*1^0.5)                                                         

d2 =       -0.356246           Hence, N(d1) = 0.3608

2.

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

=(LN(85/((85*EXP(-0.02*1))))+0.5*0.1^2*1)/(0.1*1^0.5)                                                         

d2 =       0.250000            Hence, N(d1) = 0.5987

3.                                                                    

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

=(LN(90/((85*EXP(-0.02*1))))+0.5*0.1^2*1)/(0.1*1^0.5)                                                         

d2 =       0.821584            Hence, N(d1) = 0.7943