The following prices are available for call and put options on a stock priced at $50.The risk-free rate is 6 percent and the volatility is 0.35.The March options have 90 days remaining and the June options have 180 days remaining.The Black-Scholes model was used to obtain the prices.
Use this information to answer questions 1 through 20.Assume that each transaction consists of one contract (for 100 shares)unless otherwise indicated.
For questions 7 and 8, suppose an investor expects the stock price to remain at about $50 and decides to execute a butterfly spread using the June calls.
-What will be the profit if the stock price at expiration is $52.50?
A)$171
B)$1,421
C)$1.037
D)$421
E)none of the above

Question

The following prices are available for call and put options on a stock priced at $50.The risk-free rate is 6 percent and the volatility is 0.35.The March options have 90 days remaining and the June options have 180 days remaining.The Black-Scholes model was used to obtain the prices.
  Use this information to answer questions 1 through 20.Assume that each transaction consists of one contract (for 100 shares)unless otherwise indicated.
For questions 7 and 8, suppose an investor expects the stock price to remain at about $50 and decides to execute a butterfly spread using the June calls.
-What will be the profit if the stock price at expiration is $52.50?
A)$171 
B)$1,421 
C)$1.037 
D)$421 
E)none of the above

Quizplus · Accepted Answer

To calculate profit, we first need to calculate the cost of the stock purchase.

The option cost is the premium of $3.50 multiplied by the 100 shares in the contract for a total of $350.

To exercise the option at $50.00 per share, the total cost of the stock purchase would be $5,000.

If the stock price at expiration is $52.50, the option holder can exercise the option and purchase the stock for $50.00 per share, which can then be sold for $52.50 per share.

The profit per share is $52.50 - $50.00 = $2.50.

The total profit from the contract is the profit per share multiplied by the number of shares in the contract:

$2.50 x 100 shares = $250

The profit of $250 must be reduced by the premium paid for the option:

$250 - $350 = -$100

Since the profit is negative, there is actually a loss of $100 in this scenario.

The Following Prices Are Available for Call and Put Options