CHAPTER 12
Trading Strategies Involving Options
Practice Questions
Problem 12.1.
来去海边What is meant by a protective put? What position in call options is equivalent to a protective put?
A protective put consists of a long position in a put option combined with a long position in the underlying shares. It is equivalent to a long position in a call option plus a certain amount of cash. This follows from put –call parity: 0rT p S c Ke D -+=++
歌唱家张也Problem 12.2.
Explain two ways in which a bear spread can be created.
A bear spread can be created using two call options with the same maturity and different strike prices. The investor shorts the call option with the lower strike price and buys the call option with the higher str
ike price. A bear spread can also be created using two put options with the same maturity and different strike prices. In this ca, the investor shorts the put option with the lower strike price and buys the put option with the higher strike price.
Problem 12.3.
When is it appropriate for an investor to purcha a butterfly spread?
A butterfly spread involves a position in options with three different strike prices (12K K ,, and 3K ). A butterfly spread should be purchad when the investor considers that the price of the underlying stock is likely to stay clo to the central strike price, 2K .
Problem 12.4.
Call options on a stock are available with strike prices of $15,$17.5 , and $20 and expiration dates in three months. Their prices are $4, $2, and,$0.5 respectively. Explain how the options can be ud to create a butterfly spread. Construct a table showing how profit varies with stock price for the butterfly spread.
An investor can create a butterfly spread by buying call options with strike prices of $15 and $20 and
lling two call options with strike prices of $1712. The initial investment is
11
22422$+-⨯=. The following table shows the variation of profit with the final stock price:
Problem 12.5.
What trading strategy creates a rever calendar spread?天安门
A rever calendar spread is created by buying a short-maturity option and lling a long-maturity option, both with the same strike price.
Problem 12.6.
What is the difference between a strangle and a straddle?
Both a straddle and a strangle are created by combining a long position in a call with a long position in a put. In a straddle the two have the same strike price and expiration date. In a strangle they have different strike prices and the same expiration date.
Problem 12.7.
A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Explain how a strangle can be created from the two options. What is the pattern of profits from the strangle?
A strangle is created by buying both options. The pattern of profits is as follows:
Problem 12.8.
U put –call parity to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.
A bull spread using calls provides a profit pattern with the same general shape as a bull
spread using puts (e Figures 12.2 and 12.3 in the text). Define 1p and 1c as the prices of put and call with strike price 1K and 2p and 2c as the prices of a put and call with strike price 2K . From put-call parity
111rT p S c K e -+=+
222rT p S c K e -+=+
Hence:
121221()rT p p c c K K e --=---
This shows that the initial investment when the spread is created from puts is less than the initial investment when it is created from calls by an amount 21()rT K K e --. In fact as mentioned in the text the initial investment when the bull spread is created from puts is negative, while the initial investment when it is created from calls is positive.复方蛤青片
The profit when calls are ud to create the bull spread is higher than when puts are ud by 21()(1)rT K K e ---. This reflects the fact that the call strategy involves an additional risk-free
investment of 21()rT K K e -- over the put strategy. This earns interest of
2121()(1)()(1)rT rT rT K K e e K K e ----=--.
Problem 12.9.
Explain how an aggressive bear spread can be created using put options.
An aggressive bull spread using call options is discusd in the text. Both of the options ud have relatively high strike prices. Similarly, an aggressive bear spread can be created using put options. Both of the options should be out of the money (that is, they should have relatively low strike prices). The spread then costs very little to t up becau both of the puts are worth clo to zero. In most circumstances the spread will provide zero payoff. However, there is a small chance that the stock price will fall fast so that on expiration both options will be in the money. The spread then provides a payoff equal to the difference between the two strike prices, 21K K -.
Problem 12.10.
Suppo that put options on a stock with strike prices $30 and $35 cost $4 and $7,
respectively. How can the options be ud to create (a) a bull spread and (b) a bear spread? Construct a table that shows the profit and payoff for both spreads.
月经量多是怎么回事A bull spread is created by buying the $30 put and lling the $35 put. This strategy gives ri to an initial cash inflow of $3. The outcome is as follows:
A bear spread is created by lling the $30 put and buying the $35 put. This strategy costs $3 initially. The outcome is as follows:
Problem 12.11.
U put –call parity to show that the cost of a butterfly spread created from European puts is identical to the cost of a butterfly spread created from European calls.
Define 1c , 2c , and 3c as the prices of calls with strike prices 1K , 2K and 3K . Define 1p , 2p and 3p as the prices of puts with strike prices 1K , 2K and 3K . With the usual notation 111rT c K e p S -+=+ 222rT c K e p S -+=+ 333rT c K e p S -+=+ Hence 1321321322(2)2rT c c c K K K e p p p -+-++-=+- Becau 2132K K K K -=-, it follows that 13220K K K +-= and
13213222c c c p p p +-=+-迪丽热巴图片
The cost of a butterfly spread created using European calls is therefore exactly the same as the cost of a butterfly spread created using European puts.
Problem 12.12.
A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4. Construct a table that shows the profit from a straddle. For what range of stock prices would the straddle lead to a loss?
A straddle is created by buying both the call and the put. This strategy costs $10. The profit/loss is sh
own in the following table:
This shows that the straddle will lead to a loss if the final stock price is between $50 and $70.
Problem 12.13.
Construct a table showing the payoff from a bull spread when puts with strike prices 1K and 2K with K 2>K 1 are ud.
The bull spread is created by buying a put with strike price 1K and lling a put with strike price 2K . The payoff is calculated as follows:
Problem 12.14.
房地产法律An investor believes that there will be a big jump in a stock price, but is uncertain as to the
direction. Identify six different strategies the investor can follow and explain the differences among them.
Possible strategies are:
Strangle Straddle Strip Strap
Rever calendar spread Rever butterfly spread
The strategies all provide positive profits when there are large stock price moves. A strangle is less expensive than a straddle, but requires a bigger move in the stock price in order to provide a positive profit. Strips and straps are more expensive than straddles but provide bigger profits in certain circumstances. A strip will provide a bigger profit when there is a large downward stock price move. A strap will provide a bigger profit when there is a large upward stock price move. In the ca of strangles, straddles, strips and straps, the profit
increas as the size of the stock price movement increas. By contrast in a rever calendar spread and a rever butterfly spread there is a maximum potential profit regardless of the size of th
油烟机侧吸e stock price movement.
Problem 12.15.
How can a forward contract on a stock with a particular delivery price and delivery date be created from options?
Suppo that the delivery price is K and the delivery date is T . The forward contract is created by buying a European call and lling a European put when both options have strike price K and exerci date T . This portfolio provides a payoff of T S K - under all
circumstances where T S is the stock price at time T . Suppo that 0F is the forward price. If 0K F =, the forward contract that is created has zero value. This shows that the price of a call equals the price of a put when the strike price is 0F .
Problem 12.16.
“A box spread compris four options. Two can be combined to create a long forward
position an d two can be combined to create a short forward position.” Explain this statement.
A box spread is a bull spread created using calls and a bear spread created using puts. With the notation in the text it consists of a) a long call with strike 1K , b) a short call with strike 2K , c) a long put with strike 2K , and d) a short put with strike 1K . a) and d) give a long forward contract with delivery price 1K ; b) and c) give a short forward contract with delivery price 2K . The two forward contracts taken together give the payoff of 21K K -.
Problem 12.17.
What is the result if the strike price of the put is higher than the strike price of the call in a
strangle?
The result is shown in Figure S12.1. The profit pattern from a long position in a call and a put
