To solve this problem, we need to use the Black-Scholes formula for pricing a put option. The formula is:

P = Ke^(-rt)N(-d2) - S0e^(-qt)N(-d1)

Where:
P = price of the put option
K = strike price of the option
r = risk-free interest rate
t = time to maturity
S0 = current price of the underlying asset
q = dividend yield
N = cumulative distribution function of the standard normal distribution
d1 = [ln(S0/K) + (r - q + σ^2/2)t] / σ√t
d2 = d1 - σ√t

Given the information in the problem, we have:

S0 = 10
r = 0.05
σ = 0.30
K = 12
t = 9/12 = 0.75 years
q = (1/10 + 1.4/10 + 1.8/10) / 3 = 0.42 (approx)

First, we need to calculate d1 and d2:

d1 = [ln(10/12) + (0.05 - 0.42 + 0.30^2/2)*0.75] / (0.30*√0.75) = -0.36 (approx)
d2 = -0.36 - 0.30*√0.75 = -0.65 (approx)

Then, we substitute these values into the Black-Scholes formula:

P = 12*e^(-0.05*0.75)*N(-0.65) - 10*e^(-0.42*0.75)*N(-0.36)

Using a standard normal distribution table, we find that N(-0.65) = 0.25785 and N(-0.36) = 0.35942.

P = 12*e^(-0.0375)*0.25785 - 10*e^(-0.315)*0.35942 = 2.96 (approx)

So, the price of the put option is approximately $2.96, which is not listed in the options a, b, c, or d. Therefore, the answer is d) None of the above.

Question

To solve this problem, we need to use the Black-Scholes formula for pricing a put option. The formula is:

P = Ke^(-rt)N(-d2) - S0e^(-qt)N(-d1)

Where:
P = price of the put option
K = strike price of the option
r = risk-free interest rate
t = time to maturity
S0 = current price of the underlying asset
q = dividend yield
N = cumulative distribution function of the standard normal distribution
d1 = [ln(S0/K) + (r - q + σ^2/2)t] / σ√t
d2 = d1 - σ√t

Given the information in the problem, we have:

S0 = 10
r = 0.05
σ = 0.30
K = 12
t = 9/12 = 0.75 years
q = (1/10 + 1.4/10 + 1.8/10) / 3 = 0.42 (approx)

First, we need to calculate d1 and d2:

d1 = [ln(10/12) + (0.05 - 0.42 + 0.30^2/2)*0.75] / (0.30*√0.75) = -0.36 (approx)
d2 = -0.36 - 0.30*√0.75 = -0.65 (approx)

Then, we substitute these values into the Black-Scholes formula:

P = 12*e^(-0.05*0.75)*N(-0.65) - 10*e^(-0.42*0.75)*N(-0.36)

Using a standard normal distribution table, we find that N(-0.65) = 0.25785 and N(-0.36) = 0.35942.

P = 12*e^(-0.0375)*0.25785 - 10*e^(-0.315)*0.35942 = 2.96 (approx)

So, the price of the put option is approximately $2.96, which is not listed in the options a, b, c, or d. Therefore, the answer is d) None of the above.

Knowee AI · Accepted Answer