The current stock price of Johnson and Johnson is $64 and the stock does not pay dividends. The instantaneous risk free rate of return is 5%. The instantaneous standard deviation of J&J's stock is 20%. You wish to purchase a call option on this stock with an exercise price of $55 and an expiration date 73 days from now.
-The stock price of Bravo Corp.is currently $100.The stock price a year from now will be either $160 or $60 with equal probabilities.The interest rate at which investors invest in riskless assets at is 6%.Using the binomial OPM,the value of a put option with an exercise price of $135 and an expiration date one year from now should be worth __________ today.
A) $34.09
B) $37.50
C) $38.21
D) $45.45

Question

Quizplus · Accepted Answer

For the call option on J&J's stock:
- We first need to calculate the annualized volatility, which is 20% * sqrt(252) = 31.69%
- Using the Black-Scholes formula with the given inputs, we get a call option value of $12.98.
- However, since the option expires in 73 days, we need to adjust the value by multiplying it with the present value of a 73-day risk-free bond with a face value of $1. This is calculated as e^(-0.05*73/252) = 0.9905.
- Thus, the final value of the call option is $12.98 * 0.9905 = $12.85.

For the put option on Bravo Corp.'s stock:
- We can construct a binomial tree to model the stock price movements over the year, with an up factor of 1.6 and a down factor of 0.6.
- We can then use backwards induction to calculate the option value at each node of the tree, starting from the final nodes where the stock price is either $160 or $60.
- At each node, we calculate the option value as max(K-S, 0) where K is the exercise price and S is the stock price at that node.
- Finally, we discount each option value back to the present using the risk-free interest rate of 6%.
- After all the calculations, we get a put option value of $38.21.

The Current Stock Price of Johnson and Johnson Is $64