Consider a 1-year option with exercise price $90 on a stock with annual standard

Question

Consider a 1-year option with exercise price $90 on a stock with annual standard deviation 15%. The T-bill rate is 3% per year. Find N(d1) for stock prices $85, $90, and $95. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Consider a 1-year option with exercise price $90 on a stock with annual standard deviation 15%. The T-bill rate is 3% per year. Find N(d1) for stock prices $85, $90, and $95. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Explanation / Answer

S

N(d1)

$ 85

0.1095

$ 90

0.2750

$ 95

0.4315

Option period T = 1 year

Exercise Prike K = 90

Standard Deviation = 15% or 0.15

t-bill rate r = 3% or 0.03

d1 can be calculated using the formula

d1 = ln (S/K) + ((r+ ^2/2)*T) / * Square root (T)

Where S is the current stock price

At S = 85

d1 = [ln (85/90) + (0.03 + 0.15^2/2)*1] / 0.15 * Square root (1)

       = [ln (0.944444) + (0.03 + 0.01125)*1]/0.15 * 1

       = (-0.024823583725 + 0.04125) / 0.15

      = 0.016426416275/0.15

      = 0.109509442   or 0.1095 (rounded off)

At S = 90

d1 = [ln (90/90) + (0.03 + 0.15^2/2)*1] / 0.15 * Square root (1)

       = [ln (1) + (0.03 + 0.01125)*1]/0.15 * 1

       = (0 + 0.04125) / 0.15

= 0.04125 / 0.15

= 0.275

At S = 95

d1 = [ln (95/90) + (0.03 + 0.15^2/2)*1] / 0.15 * Square root (1)

       = [ln (1.055556) + (0.03 + 0.01125)*1]/0.15 * 1

       = [0.0234810958495 + 0.04125)/0.15

      = 0.0647310958495/0.15

     = 0.4315406 or 0.4315 (rounded off)

S

N(d1)

$ 85

0.1095

$ 90

0.2750

$ 95

0.4315

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