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 (a) $55, (b) $60, and (c) $65.

Answer 1

Case 1: 0.4266

Case 2: 0.5987

Case 3: 0.7422

Step-by-step explanation:

We will use the following formula to find d1 which is also given in the attachment below:

d1 = [ ln(S/K) + (r + 0.5 * s^2)*t ] / s * √t

Here

K is strike price and is $60

r is risk free rate which is 3%

s is annual standard deviation which is 20%

t is the option period which is 1 one year

Case 1: Stock Price is $55

Here K is $55. Putting values in the above equation, we have:

d1 = [ ln(55/60) + (3% + 0.5 * 20%^2)*1 ] / 20% * √1

d1 = -0.1851

By using the normal distribution table, we can calculate N(d1) which is:

N(d1) = 0.4266

Case 2: Stock Price is $60

Here K is $60. Putting values in the above equation, we have:

d1 = [ ln(60/60) + (3% + 0.5 * 20%^2)*1 ] / 20% * √1

d1 = 0.25

By using the normal distribution table, we can calculate N(d1) which is:

N(d1) = 0.5987

Case 3: Stock Price is $65

Here K is $65. Putting values in the above equation, we have:

d1 = [ ln(65/60) + (3% + 0.5 * 20%^2)*1 ] / 20% * √1

d1 = 0.6502

By using the normal distribution table, we can calculate N(d1) which is:

N(d1) = 0.7422