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An Introduction to Derivatives and Risk Management: With Stock-Trak Coupon

Don M. Chance, Robert Brooks

Chapter 7

Advanced Option Scrategies - all with Video Answers

Educators

Chapter Questions

Problem 1

Suppose that you are following the stock of a firm that has been experiencing severe problems. Failure is imminent unless the firm is granted governmentguaranteed loans. If the firm fails, its stock will, of course, fall substantially. If the loans are granted, it is expected that the stock will rise substantially. Identify two strategies that would be appropriate for this situation. Justify your answers.

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Problem 2

Explain how a short call added to a protective put forms a collar and how it changes the payoff and up-front cost.

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03:33

Problem 3

Derive the profit equations for a put buil spread. Determine the maximum and minimum profits and the breakeven stock price at expiration.

Zach Steedman
Zach Steedman
Numerade Educator

Problem 4

Explain the process by which the profit of a short straddle closed out prior to expiration is influenced by the time values of the put and call.

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Problem 5

The chapter showed how analyzing a box spread is like a capital budgeting problem using the net present value approach. Consider the internal rate of return method of examining capital budgeting problems and analyze the box spread in that context.

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Problem 6

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Construct a bear money spread using the October 165 and 170 calls. Hold the position until the options expire. Determine the profits and graph the results. Identify the breakeven stock price at expiration and the maximum and minimum profits. Discuss any special considerations associated with this strategy.

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Problem 7

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Repeat problem 6, but close the position on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify the approximate breakeven stock price.

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Problem 8

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Construct a collar using the October 160 put. First use the Black-Scholes-Merton model to identify a call that will make the collar have zero up-front cost. Then close the position on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify the approximate breakeven stock price. Determine the maximum and minimum profits.

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Problem 9

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Suppose that you are expecting the stock price to move substantially over the next three months. You are considering a butterfly spread. Construct an appropriate butterfly spread using the October 160,165 , and 170 calls. Hold the position until expiration. Determine the profits and graph the results. Identify the two breakeven stock prices and the maximum and minimum profits.

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Problem 10

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Construct a calendar spread using the August and October 170 calls that will profit from high volatility. Close the position on August 1. Use the spreadsheet to find the profits for the possible stock prices on August 1. Generate a graph and use it to estimate the maximum and minimum profits and the breakeven stock prices.

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Problem 11

Using the Black-Scholes-Merton model, compute and graph the time value decay of the October 165 call on the following dates: July 15, July 31, August 15, August 31 , September 15, September 30 , and October 16. Assume that the stock price remains constant. Use the spreadsheet to find the time value in all of the cases.

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Problem 12

Consider a riskless spread with a long position in the August 160 call and a short position in the October 160 call. Determine the appropriate hedge ratio. Then show how a $\$ 1$ stock price increase would have a neutral effect on the spread value. Discuss any limitations of this procedure.

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Problem 13

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Construct a long straddle using the October 165 options. Hold until the options expire. Determine the profits and graph the results. Identify the breakeven stock prices at expiration and the minimum profit.

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Problem 14

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
Repeat problem 13, but close the positions on September 20. Use the spreadsheet to find the profits for the possible stock prices on September 20. Generate a graph and use it to identify the approximate breakeven stock prices.

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Problem 15

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
A slight variation of a straddle is a strap, which uses two calls and one put. Construct a long strap using the October 165 options. Hold the position until expiration. Determine the profits and graph the results. Identify the breakeven stock prices at expiration and the minimum profit. Compare the results with the October 165 straddle.

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Problem 16

The following option prices ruere observed for calls and puts on a stock on $J$ thly 6 of a perticutar year. Use this information for prollems 6 through 20. The stock was friced al 165.13. The expirations are July 17, August 21, and October 16. The continuously compounded rish-free rates associated with: the three expirations are $0.0503,0.0535$, and 0.0571 , respectively. The standard deviation is 0.21 .
For problens 6 through 10 and 13 through 16 , determine the profits for the holding period indicated for passible stock prices of $150,155,160,165,170,175$, and 180 at the end of the holding period. Ansuer any other quiestions as indicated. Note: Your Excel spreadsheet Stratlyz7e, xls will be useful here for obtaining graphs as requested but it does not allow you to calculate the profits for several user-specified asset prices. It permits you to specify one asset price and a maximum and minimum. Use Stratlyz7e.xls to produce the graph for the range of prices from 150 to 180 but determine the profuts for the prices of $150,155, \ldots, 180 \mathrm{by}$ hand for positions held to expiration. For pasitions clased prior to expiration, use the spreadshet BSMbin7e.xls or the Windous program BSMbwin 7e,exe to determine the option price when the position is clased; then calculate the profut by hand.
(TABLE CAN'T COPY)
A strip is a variation of a straddle involving two puts and one call. Construct a short strip using the August 170 options. Hold the position until the options expire. Determine the profits and graph the results. Identify the breakeven stock prices at expiration and the minimum profit.

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00:23

Problem 17

Analyze the August $160 / 170$ box spread. Determine whether a profit opportunity exists and, if so, how one should exploit it.

Amrita Bhasin
Amrita Bhasin
Numerade Educator
02:52

Problem 18

Complete the following table with the correct formula related to various spread strategies.
(TABLE CAN'T COPY)

Joanna Josey
Joanna Josey
Numerade Educator
02:52

Problem 19

Complete the following table with the correct formula related to various spread strategies.
(TABLE CAN'T COPY)

Joanna Josey
Joanna Josey
Numerade Educator

Problem 20

(Concept Problem) Many option traders use a combination of a money spread and a calendar spread called a diagonal spread. This transaction involves the purchase of a call with a lower exercise price and longer time to expiration and the sale of a call with a higher exercise price and shorter time to expiration. Evaluate the diagonal spread that involves the purchase of the October 165 call and the sale of the August 170 call. Determine the profits for the same stock prices you previously examined under the assumption that the position is closed on August 1. Use the spreadsheet to find the profits for the possible stock prices on August 1. Generate a graph and use it to estimate the breakeven stock price at the end of the hoiding period.

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Problem 21

(Concept Problem) Another variation of the straddle is called a strangie. A strangle is the purchase of a call with a higher exercise price and a put with a lower exercise price. Evaluate the strangle strategy by examining the purchase of the August 165 put and $170 \mathrm{call}$. As in the problems above, determine the profits for stock prices of $150,155,160,165,170,175$, and 180 . Hold the position until expiration and graph the results. Find the breakeven stock prices at expiration. Explain why one would want to use a strangle.

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Problem 22

Explain why option traders often use spreads instead of simple long or short options and combined positions of options and stock.

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Problem 23

Suppose that an option trader has a call bull spread. The stock price has risen substantially, and the trader is considering closing the position early. What factors should the trader consider with regard to closing the transaction before the options expire?

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01:24

Problem 24

Explain why a straddle is not necessarily a good strategy when the underlying event is well known to everyone.

Rashmi Sinha
Rashmi Sinha
Numerade Educator