Question

The current stock price of Johnson & Johnson is $72, and the stock does not pay dividends. The instantaneous risk-free rate of return is 3%. The instantaneous standard deviation of J&J's stock is 40%. You want to purchase a call option on this stock with an exercise price of $63 and an expiration date 57 days from now. Using the Black-Scholes OPM, the put option should be worth __________ today. 1.05 1.12 10.05 10.41

Answer 1

The value of the put option on Johnson & Johnson's stock with an exercise price of $63 and an expiration date 57 days from now is approximately $1.12, calculated using the Black-Scholes option pricing model. The correct option is B).

To calculate the value of the put option using the Black-Scholes option pricing model, we need the following inputs

Current stock price (S): $72

Exercise price (X): $63

Time to expiration (T): 57 days (convert to years by dividing by 365: 57/365 ≈ 0.156)

Risk-free rate (r): 3% (convert to decimal: 0.03)

Volatility (σ): 40% (convert to decimal: 0.4)

Using the Black-Scholes formula for put options

d1 = [ln(S/X) + (r + (σ²)/2) * T] / (σ * √(T))

d2 = d1 - σ * √(T)

N(-d1) and N(-d2) are the cumulative standard normal distribution values for -d1 and -d2, respectively.

Put option value (P) = X *
`e^(-rT)` * N(-d2) - S * N(-d1)

Now let's calculate step by step:

Calculate d1:

d1 = [ln(72/63) + (0.03 + (0.4²)/2) * 0.156] / (0.4 * √(0.156))

≈ 0.760

Calculate d2:

d2 = 0.760 - 0.4 * √(0.156)

≈ 0.638

Calculate N(-d1) and N(-d2):

Using standard normal distribution tables or a calculator, we find N(-d1) ≈ 0.223 and N(-d2) ≈ 0.264.

Calculate the put option value (P):

P = 63 *
`e^(-0.03* 0.156)`* 0.264 - 72 * 0.223

≈ 1.12

Therefore, the value of the put option today is approximately $1.12.The correct answer is B).