Question

Consider a 1-year option with exercise price $125 on a stock with annual standard deviation 10%. The T-bill rate is 3% per year. Find N(d₁) for stock prices (a) $120, (b) $125, and (c) $130. (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Answer 1

d1 = (ln(S0 / K) + (r + σ2/2)*T) / σ√T

S0 = current spot price

K = strike price

N(x) is the cumulative normal distribution function

r = risk-free interest rate

T is the time to expiry in years

σ = standard deviation of underlying stock returns

(a)

We calculate d1 as below :

· ln(S0 / K) = ln(120 / 125). We input the same formula into Excel, i.e. =LN(120 / 125)

· (r + σ2/2)*T = (0.03 + (0.102/2)*1

· σ√T = 0.10 * √1

d1 = -0.0582

N(d1) is calculated in Excel using the NORMSDIST function and inputting the value of d1 into the function.

N(d1) = 0.4768

(b)

We calculate d1 as below :

· ln(S0 / K) = ln(125 / 125). We input the same formula into Excel, i.e. =LN(125 / 125)

· (r + σ2/2)*T = (0.03 + (0.102/2)*1

· σ√T = 0.10 * √1

d1 = 0.3500

N(d1) is calculated in Excel using the NORMSDIST function and inputting the value of d1 into the function.

N(d1) = 0.6368

(c)

We calculate d1 as below :

· ln(S0 / K) = ln(130 / 125). We input the same formula into Excel, i.e. =LN(130 / 125)

· (r + σ2/2)*T = (0.03 + (0.102/2)*1

· σ√T = 0.10 * √1

d1 = 0.7422

N(d1) is calculated in Excel using the NORMSDIST function and inputting the value of d1 into the function.

N(d1) = 0.7710