Consider a 1-year option with exercise price $60 on a stock with annual standard

Question

Consider a 1-year option with exercise price $60 on a stock with annual standard deviation 20%. The T-bill rate is 3% per year. Find N(d1) for stock prices $55, $60, and $65. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Consider a 1-year option with exercise price $60 on a stock with annual standard deviation 20%. The T-bill rate is 3% per year. Find N(d1) for stock prices $55, $60, and $65. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Explanation / Answer

S0 = underlying price (USD per share)

X = strike price (USD per share)

= volatility (% p.a.)

r = continuously compounded risk-free interest rate (% p.a.)

q = continuously compounded dividend yield (% p.a.)

t = time to expiration (% of year)

N(d1) at $55:

d1 = [ln($55/$60) + 1*(0.03-0 + .04/2)] / 0.2*(1)0.5
= 0.2122

N(d1) = 0.58403

N(d1) at $60:

d1 = [ln($60/$60) + 1*(0.03-0 + .04/2)] / 0.2*(1)0.5
= 0.25

N(d1) = 0.59870

N(d1) at $65:

d1 = [ln($65/$60) + 1*(0.03-0 + .04/2)] / 0.2*(1)0.5
= 0.28476

N(d1) = 0.612087

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