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.
Answer questions 18 through 20 about a long box spread using the June 50 and 55 options.
-What is the net present value of the box spread?
A)$9.84
B)$5.00
C)$16.00
D)$1.84
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.
Answer questions 18 through 20 about a long box spread using the June 50 and 55 options.
-What is the net present value of the box spread?
A)$9.84 
B)$5.00 
C)$16.00 
D)$1.84 
E)none of the above

Quizplus · Accepted Answer

The box spread involves buying a call option and selling a put option at one strike price while simultaneously selling a call option and buying a put option at a higher strike price, all with the same expiration date. This strategy is designed to result in a riskless profit equal to the difference in strike prices minus the initial cost of entering the positions. In this scenario, the initial cost is $118.16, and the difference in strike prices is $120.

Therefore, the net present value of the box spread is ($120 - $118.16) = $1.84. Choice D is the correct answer.

The Following Prices Are Available for Call and Put Options