Question

Consider a 1-year option with exercise price $40 on a stock with annual standard deviation 15%. The T-bill rate is 2% per year. Find N(d1) for stock prices $35, $40, and $45.

Answer 1

Formula as per Black Scholes model,

N(d_{​​​​​​1}​​​​​) = [ln (stock price/exercise price) + (r + {6²/2})t ] / (6* √t)

given in question, where

r = T bill rate = 2% = 0.02

t = 1 year

6= standard deviation = 15% = .15

6² = (0.15)² = 0.0225

A)

= [($35/$40) + (0.02 + (0.0225/2))* 1]/ (0.15*1)

= (0.875 + 0.03125) / 0.15

= $ 6.0416

B)

= [($40/$40) + (0.02 + (0.0225/2))*1] / (0.15*1)

= (1 + 0.03125) / 0.15

= $6.875

C)

= [($45/$40) + (0.02 + (0.0225/2))*1] / (0.15*1)

= (1.125 + 0.03125) / 0.15

= $ 7.7083