Question

Consider a 1-year option with exercise price $110 on a stock with annual standard deviation 10%. The T-bill rate is 3% per year. Find N(d1) for stock prices $105, $110, and $115.

If you could explain the difference between D and N(d1) that would be great. I think that is where im getting stuck

Answer 1

Strike Price(K) = 110
Risk free rate(r) =3%
Standard Deviation (s)=10%

At stock price(S) =105
Formula for D1 =(Ln(S/K)+(r+s²/2)*t)/(s*t^0.5) =(ln(105/100)+(3%^2+10%^2/2)*1)/(10%*1^0.5)=0.5469
N(d1) can be found out using excel formula =NORMSDIST(0.5469) =0.7078
N(d1) can also be found from cumulative distribution table where d1 is used in place of z vale

At stock price(S) =110
Formula for D1 =(Ln(S/K)+(r+s²/2)*t)/(s*t^0.5) =(ln(110/100)+(3%^2+10%^2/2)*1)/(10%*1^0.5)=1.0121
N(d1) can be found out using excel formula =NORMSDIST(1.0121) =0.8443

At stock price(S) =115
Formula for D1 =(Ln(S/K)+(r+s²/2)*t)/(s*t^0.5) =(ln(115/100)+(3%^2+10%^2/2)*1)/(10%*1^0.5)=1.0121
N(d1) can be found out using excel formula =NORMSDIST(1.4566) =0.9274