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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

A stock price is currently $50. It is known that at the end of 2 months it will be either $53 or $48. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a
Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tree. Explain why it is not possible to set up a position in the stock
What are the formulas for u and d in terms of volatility?
For the situation considered in Problem 12.5, what is the value of a 1-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put-call
A stock price is currently $100. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What
A stock price is currently $50. It is known that at the end of 6 months it will be either $45 or $55. The risk-free interest rate is 10% per annum with continuous compounding. What is the value of a
What is meant by the "delta" of a stock option?
Explain the nc-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree.
A stock price is currently $40. It is known that at the end of 1 month it will be either $42 or $38. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a
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%
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
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
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
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
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
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.
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 11.1, have to last for it to
One Australian dollar 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
What is the result if the strike price of the put is higher than the strike price of the call in a strangle?
"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.
How can a forward contract on a stock with a particular delivery price and delivery date be created from options?
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
Construct a table showing the payoff from a bull spread when puts with strike prices K and K2, with K > K, are used.
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
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.
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
Explain how an aggressive bear spread can be created using put options.
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.
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
What is the difference between a strangle and a straddle?
What trading strategy creates a reverse calendar spread?
Call options on a stock are available with strike prices of $15, $17, and $20, and expiration dates in 3 months. Their prices are $4, $2, and $4, respectively. Explain how the options can be used to
When is it appropriate for an investor to purchase a butterfly spread?
Explain two ways in which a bear spread can be created.
What is meant by a protective put? What position in call options is equivalent to a protective put‘?
Consider a put option on a non-dividend-paying stock when the stock price is $40, the strike price is $42, the risk-free interest rate is 2%, the volatility is 25 % per annum, and the time to
Consider an option on a stock when the stock price is $41, the strike price is $40, the risk-free rate is 6%, the volatility is 35%, and the time to maturity is 1 year. Assume that a dividend of
Suppose that you are the manager and sole owner of a highly leveraged company. All the debt will mature in 1 year. If at that time the value of the company is greater than the face value of the debt,
What is the result corresponding to that in Problem 10.23 for European put options?
Suppose that c1, C2, and c3 are the prices of European call options with strike prices K1, K2, and K3, respectively, where K3 > K2 > K1 and K3 — K2 = K2 - K1. All options have the same maturity.
A European call option and put option on a stock both have a strike price of $20 and an expiration date in 3 months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock
Consider a 5-year call option on a non-dividend-paying stock granted to employees. The option can be exercised at any time after the end of the first year. Unlike a regular exchange-traded call
Prove the result in equation (10.11). (Hint: For the first part of the relationship, consider (a) a portfolio consisting of a European call plus an amount of cash equal to D+K, and (b) a portfolio
Prove the result in equation (10.7). (Hint: For the first part of the relationship, consider (a) a portfolio consisting of a European call plus an amount of cash equal to K, and (b) a portfolio
Explain carefully the arbitrage opportunities in Problem 10.16 if the American put price is greater than the calculated upper bound.
The price of an American call on a non-dividend-paying stock is $4. The stock price is $31, the strike price is $30, and the expiration date is in 3 months. The risk-free interest rate is 8%. Derive
Explain the arbitrage opportunities in Problem 10.14 if the European put price is $3.
The price of a European call that expires in 6 months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in 2 months and again in 5 months.
Give an intuitive explanation of why the early exercise of an American put becomes more attractive as the risk-free rate increases and volatility decreases.
A 1-month European put option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What
A 4-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in 1 month. The risk-free
What is a lower bound for the price of a 2-month European put option on a non- dividend-paying stock when the stock price is $58, the strike price is $65, and the risk- free interest rate is 5% per
What is a lower bound for the price of a 6-month call option on a non-dividend-paying stock when the stock price is $80, the strike price is $75, and the risk-free interest rate is 10% per annum?
Explain why the arguments leading to put-call parity for European options cannot be used to give a similar result for American options.
The price of a non-dividend-paying stock is $19 and the price of a 3-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. What is the price of
Why is an American call option on a dividend-paying stock always worth at least as much as its intrinsic value. Is the same true of a European call option? Explain your answer.
"The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put." Explain this statement.
Give two reasons why the early exercise of an American call option on a non-dividend- paying stock is not optimal. The first reason should involve the time value of money. The second should apply
What is a lower bound for the price of a 1-month European put option on a non- dividend-paying stock when the stock price is $12, the strike price is $15, and the risk- free interest rate is 6% per
What is a lower bound for the price of a 4-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
List the six factors that affect stock option prices.
On July 20, 2004, Microsoft surprised the market by announcing a $3 dividend. The exdividend date was November 17, 2004, and the payment date was December 2, 2004. Its stock price at the time was
“If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense.” Discuss this viewpoint. Can you think
The price of a stock is $40. The price of a 1-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a 1-year European call option on the stock with a
A United States investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
Explain why the market maker's bid-offer spread represents a real cost to options investors.
Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, and (c) August 5?
What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price?
"If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months." Discuss this statement.
Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in 4 months. Explain how the terms of the option contract change when there is: (a) a 10%
The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation's foreign exchange risk. Discuss the advantages and disadvantages of each.
Explain carefully the difference between writing a put option and buying a call option.
Explain why an American option is always worth at least as much as its intrinsic value.
Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.
A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing
Describe the terminal value of the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the
Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a
Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances
A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) NASDAQ OMX and (b) the over-the-counter market for trading?
"Employee stock options issued by a company are different from regular exchange-traded call options on the company's stock because they can affect the capital structure of the company." Explain this
A company declares a 2-for-1 stock split. Explain how the terms change for a call option with a strike price of $60.
A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1 and (b) May 30?
Explain why margins are required when clients write options but not when they buy options.
An investor sells a European call option with strike price of K and maturity T and buys a put with the same strike price and maturity. Describe the investor's position.
An investor sells a European call on a share for $4. The stock price is $47 and the strike price is $50. Under what circumstances does the investor make a profit? Under what circumstances will the
An investor buys a European put on a share for $3. The stock price is $42 and the strike price is $40. Under what circumstances does the investor make a profit? Under what circumstances will the
Investigate what happens as the width of the mezzanine tranche of the ABS in Figure 8.3 is decreased with the reduction of mezzanine tranche principal being divided equally between the equity and
Suppose that the principal assigned to the senior, mezzanine, and equity tranches is 70%, 20%, and 10% for both the ABS and the ABS CDO in Figure 8.3. What difference does this make to Table 8.1?
Explain why the end-of-year bonus is sometimes referred to as "short-term compensation."
Explain why the AAA-rated tranche of an ABS CDO is more risky than the AAA-rated tranche of an ABS.
Explain the impact of an increase in default correlation on the risks of the senior tranche of an ABS. What is its impact on the risks of the equity tranche?
How is an ABS CDO created? What was the motivation to create ABS CDOs?
What is meant by the term "agency costs"? How did agency costs play a role in the credit crisis?
How were the risks in ABS CDOS misjudged by the market?
Why did mortgage lenders frequently not check on information provided by potential borrowers on mortgage application forms during the 2000 to 2007 period?
Why do you think the increase in house prices during the 2000 to 2007 period is referred to as a bubble?
What is a subprime mortgage?
What are the numbers in Table 8.1 for a loss rate of (a) 12% and (b) 15%?
What is the waterfall in a securitization?
What is a mezzanine tranche?

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