Use putcall parity to show that the cost of a butterfly spread created from European

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

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

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

Call options on a stock are available with strike prices of $15, $171 2 , and $20, and expiration dates in 3 months. Their prices are $4, $2, and $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.

What trading strategy creates a reverse calendar spread?

What is the difference between a strangle and a straddle?

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?

Use putcall parity to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.

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

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.

Use putcall 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.

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?

Construct a table showing the payoff from a bull spread when puts with strike prices K1 and K2, with K2 > K1, are used.

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.

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

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

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

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.

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.

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.

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?

Three put options on a stock have the same expiration date and strike prices of $55, $60, and $65. The market prices are $3, $5, and $8, respectively. Explain how a butterfly 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?

A diagonal spread is created by buying a call with strike price K2 and exercise date T2 and selling a call with strike price K1 and exercise date T1, where T2 > T1. Draw a diagram showing the profit at time T1 when (a) K2 > K1 and (b) K2 < K1.

Draw a diagram showing the variation of an investors 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.

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.

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.

Describe the trading position created in which a call option is bought with strike price K2 and a put option is sold with strike price K1 when both have the same time to maturity and K2 > K1. What does the position become when K1 K2?

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.