Chapter 12, Trading strategies involving options Video Solutions, Options, Futures, and Other Derivatives

01:26

Problem 1

What is meant by a protective put? What position in call options is equivalent to a protective put?

Jennifer Stoner

Numerade Educator

02:32

Problem 2

Explain two ways in which a bear spread can be created.

Carlene Jimenez

Numerade Educator

Problem 3

When is it appropriate for an investor to purchase a butterfly spread?

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Call options on a stock are available with strike prices of $$\$ 15, \$ 17 \frac{1}{2}$$, and $$\$ 20$$, and expiration dates in 3 months. Their prices are $$\$ 4, \$ 2$$, and $$\$ \frac{1}{2}$$, respectively. Explain how the options can be used to create a butterfly spread. Construct a table showing how profit varies with stock price for the butterfly spread.

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Problem 5

What trading strategy creates a reverse calendar spread?

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03:18

Problem 6

What is the difference between a strangle and a straddle?

Sanu Kumar

Numerade Educator

Problem 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 these two options. What is the pattern of profits from the strangle?

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Problem 8

Use 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.

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Problem 9

Explain how an aggressive bear spread can be created using put options.

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Problem 10

Suppose that put options on a stock with strike prices $$\$ 30$$ and $$\$ 35$$ cost $$\$ 4$$ and $$\$ 7$$, respectively. How can the options be used to create (a) a bull spread and (b) a bear spread? Construct a table that shows the profit and payoff for both spreads.

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Problem 11

Use 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.

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Problem 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?

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Problem 13

Construct a table showing the payoff from a bull spread when puts with strike prices $K_1$ and $K_2$, with $K_2>K_1$, are used.

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Problem 14

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.

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Problem 15

How can a forward contract on a stock with a particular delivery price and delivery date be created from options?

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Problem 16

"A box spread comprises four options. Two can be combined to create a long forward position and two to create a short forward position." Explain this statement.

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03:34

Problem 17

What is the result if the strike price of the put is higher than the strike price of the call in a strangle?

Jonathan Tapiwa

Numerade Educator

Problem 18

A foreign currency is currently worth $$\$ 0.64$$. A 1-year butterfly spread is set up using European call options with strike prices of $$\$ 0.60, \$ 0.65$$, and $$\$ 0.70$$. The risk-free interest rates in the United States and the foreign country are $5 \%$ and $4 \%$ respectively, and the volatility of the exchange rate is $15 \%$. Use the DerivaGem software to calculate the cost of setting up the butterfly spread position. Show that the cost is the same if European put options are used instead of European call options.

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Problem 19

An index provides a dividend yield of $1 \%$ and has a volatility of $20 \%$. The risk-free interest rate is $4 \%$. How long does a principal-protected note, created as in Example 12.1, have to last for it to be profitable for the bank issuing it? Use DerivaGem.

Rashmi Sinha

Numerade Educator

08:00

Problem 20

Explain the statement at the end of Section 12.1 that, when dividends are zero, the principal protected note cannot be profitable for the bank no matter how long it lasts.

Md.Daniyal Arshad

Numerade Educator

Problem 21

A trader creates a bear spread by selling a 6-month put option with a $$\$ 25$$ strike price for $$\$ 2.15$$ and buying a 6-month put option with a $$\$ 29$$ strike price for $$\$ 4.75$$. What is the initial investment? What is the total payoff (excluding the initial investment) when the stock price in 6 months is (a) $$\$ 23$$, (b) $$\$ 28$$, and (c) $$\$ 33$$.

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Problem 22

A trader sells a strangle by selling a 6-month European call option with a strike price of $$\$ 50$$ for $$\$ 3$$ and selling a 6-month European put option with a strike price of $$\$ 40$$ for $$\$ 4$$. For what range of prices of the underlying asset in 6 months does the trader make a profit?

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Problem 23

spread can be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?

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Problem 24

A diagonal spread is created by buying a call with strike price $K_2$ and exercise date $T_2$ and selling a call with strike price $K_1$ and exercise date $T_1$, where $T_2>T_1$. Draw a diagram showing the profit from the spread at time $T_1$ when (a) $K_2>K_1$ and (b) $K_2<K_1$.

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Problem 25

Draw a diagram showing the variation of an investor's profit and loss with the terminal stock price for a portfolio consisting of:
(a) One share and a short position in one call option
(b) Two shares and a short position in one call option
(c) One share and a short position in two call options
(d) One share and a short position in four call options.
In each case, assume that the call option has an exercise price equal to the current stock price.

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Problem 26

Suppose that the price of a non-dividend-paying stock is $$\$ 32$$, its volatility is $30 \%$, and the risk-free rate for all maturities is $5 \%$ per annum. Use DerivaGem to calculate the cost of setting up the following positions:
(a) A bull spread using European call options with strike prices of $$\$ 25$$ and $$\$ 30$$ and a maturity of 6 months
(b) A bear spread using European put options with strike prices of $$\$ 25$$ and $$\$ 30$$ and a maturity of 6 months
(c) A butterfly spread using European call options with strike prices of $$\$ 25$$, $$\$ 30$$, and $$\$ 35$$ and a maturity of 1 year
(d) A butterfly spread using European put options with strike prices of $$\$ 25$$, $$\$ 30$$, and $$\$ 35$$ and a maturity of 1 year
(e) A straddle using options with a strike price of $$\$ 30$$ and a 6 -month maturity
(f) A strangle using options with strike prices of $$\$ 25$$ and $$\$ 35$$ and a 6-month maturity.
In each case provide a table showing the relationship between profit and final stock price. Ignore the impact of discounting.

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Problem 27

What trading position is created from a long strangle and a short straddle when both have the same time to maturity? Assume that the strike price in the straddle is halfway between the two strike prices of the strangle.

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04:10

Problem 28

Describe the trading position created in which a call option is bought with strike price $K_2$ and a put option is sold with strike price $K_1$ when both have the same time to maturity and $K_2>K_1$. What does the position become when $K_1=K_2$ ?

Narayan Hari

Numerade Educator

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Problem 29

A bank decides to create a five-year principal-protected note on a non-dividend-paying stock by offering investors a zero-coupon bond plus a bull spread created from calls. The risk-free rate is $4 \%$ and the stock price volatility is $25 \%$. The low-strike-price option in the bull spread is at the money. What is the maximum ratio of the high strike price to the low strike price in the bull spread. Use DerivaGem.

Rashmi Sinha

Numerade Educator

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