Question

 

The current stock price of Johnson & Johnson is $178, and the stock does not pay dividends. The instantaneous risk-free rate of return is 6%. The instantaneous standard deviation of J&J's stock is 30%. You want to purchase a put option on this stock with an exercise price of $171 and an expiration date 60 days from now. Assume 365 days in a year. With this information, you calculate the probability that a random draw from a standard normal distribution will be less that d1, aka N(d1), as 0.68145 and the N(d2) as 0.63687.

 

Using Black-Scholes, the put option should be worth ______ today.

Answer 1

The question requires the valuation of a put option using Black Scholes Option Pricing Model (BSOPM).

 

The BSOPM in its most original form was a model to value the call options on a non dividend paying stock. Subsequently it has been modified to value put options, options on dividend paying stocks and various exotic options as well.

 

Five key inputs are required in the model: Current stock price, strike price, time to maturity, volatility and risk free rate.

 

Current stock price, S0=178

Risk free rate, r = 6%

Standard deviation, σ = 30%

Strike price, K = 171

Years to maturity, t = 60/365 = 12/73

N(d1) = 0.68145

N(d2) = 0.63687

 

All the inputs are available with us.

 

Hence, the value of the put option is $ 4.78.

Hence, the value of the put option is $ 4.78.