USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The current stock price of ABC Corporation is $53.50. ABC Corporation has the following put and call option prices that expire six months from today. The risk-free rate of return is 5 percent, and the expected return on the market is 11 percent.

-Refer to Exhibit 14.4. What is the value of a synthetic stock created with put and call options that expire in six months with an expiration price of $50?
A) $53.04
B) $53.53
C) $54.54
D) $55.03
E) $56.23

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
The current stock price of ABC Corporation is $53.50. ABC Corporation has the following put and call option prices that expire six months from today. The risk-free rate of return is 5 percent, and the expected return on the market is 11 percent.
 
-Refer to Exhibit 14.4. What is the value of a synthetic stock created with put and call options that expire in six months with an expiration price of $50?
A) $53.04 
B) $53.53 
C) $54.54 
D) $55.03 
E) $56.23

Quizplus · Accepted Answer

To create a synthetic stock using put and call options, we need to buy a call option and sell a put option with the same expiration price and date. 
Buying a call option at $50 strike price will cost us $4.81 [(max(0, current stock price - strike price) - option premium) / (1 + risk-free rate) ^ time] 
Selling a put option at $50 strike price will give us a premium of $2.27 [(max(0, strike price - current stock price) - option premium) / (1 + risk-free rate) ^ time] 
Therefore, the net cost of creating a synthetic stock is $2.54 ($4.81 - $2.27). 
The value of the synthetic stock today will be the current stock price plus the net cost, which is $56.04 ($53.50 + $2.54). 
Therefore, the value of a synthetic stock created with put and call options that expire in six months with an expiration price of $50 is $53.04 (the current stock price minus the net cost).