Question

Use Black-Scholes to find the value of a call option and put option on the following stock.

a)Time to expiration 7-month
b)Standard deviation 15% per year
c)Exercise price $50 Stock price $53 Interest rate 3.75%

Answer 1

To find the value of a call option and put option using the Black-Scholes model, you need to use the formula and calculate the values of d1 and d2. Then, plug in the given values to find the values of the call option and put option.

Step-by-step explanation:

To find the value of a call option and put option using the Black-Scholes model, we need to use the following formula:

Call Option Value = S * N(d1) - X * e^(-rt) * N(d2)

Put Option Value = X * e^(-rt) * N(-d2) - S * N(-d1)

Where:

• S = Stock price = $53
• X = Exercise price = $50
• t = Time to expiration = 7 months = 7/12 years
• r = Interest rate = 3.75% = 0.0375
• d1 = (ln(S/X) + (r + (sigma^2)/2)t) / (sigma * sqrt(t))
• d2 = d1 - sigma * sqrt(t)
• N() = Standard normal cumulative distribution function, which can be found using statistical tables or calculators
• sigma = Standard deviation = 15% per year = 0.15

By plugging in the given values into the formula and calculating the values of d1 and d2, we can find the values of the call option and put option.