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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

A futures price is currently 50. At the end of 6 months it will be either 56 or 46. The risk- free interest rate is 6% per annum. What is the value of a 6-month European call option with a strike
Calculate the value of a 5-month European put futures option when the futures price is $19, the strike price is $20, the risk-free interest rate is 12% per annum, and the volatility of the futures
A total return index tracks the return, including dividends, on a certain portfolio. Explain how you would value (a) forward contracts and (b) European options on the index.AppendixLO1
The S&P 100 index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the
What is the put-call parity relationship for European currency options?AppendixLO1
A foreign currency is currently worth $1.50. The domestic and foreign risk-free interest rates are 5% and 9%, respectively. Calculate a lower bound for the value of a 6-month call option on the
Consider a stock index currently standing at 250. The dividend yield on the index is 4% per annum and the risk-free rate is 6% per annum. A 3-month European call option on the index with a strike
Would you expect the volatility of a stock index to be greater or less than the volatility of a typical stock? Explain your answer.AppendixLO1
Does the cost of portfolio insurance increase or decrease as the beta of the portfolio increases? Explain your answer.AppendixLO1
Suppose that a portfolio is worth $60 million and the S&P 500 is at 1200. If the value of the portfolio mirrors the value of the index, what options should be purchased to provide protection against
Consider again the situation in Problem 14.21. Suppose that the portfolio has a beta of 2.0, that the risk-free interest rate is 5% per annum, and that the dividend yield on both the portfolio and
Suppose you buy a put option contract on October gold futures with a strike price of $400 per ounce. Each contract is for the delivery of 100 ounces. What happens if you exercise when the October
Suppose you sell a call option contract on April live-cattle futures with a strike price of 70 cents per pound. Each contract is for the delivery of 40,000 pounds. What happens if the contract is
Consider a 2-month call futures option with a strike price of 40 when the risk-free interest rate is 10% per annum. The current futures price is 47. What is a lower bound for the value of the futures
Consider a 4-month put futures option with a strike price of 50 when the risk-free interest rate is 10% per annum. The current futures price is 47. What is a lower bound for the value of the futures
A futures price is currently 60. It is known that over each of the next two 3-month periods it will either rise by 10% or fall by 10%. The risk-free interest rate is 8% per annum. What is the value
In Problem 14.27, what is the value of a 6-month European put option on futures with a strike price of 60? If the put were American, would it ever be worth exercising it early? Verify that the call
A futures price is currently 25, its volatility is 30% per annum, and the risk-free interest rate is 10% per annum. What is the value of a 9-month European call on the futures with a strike price of
A futures price is currently 70, its volatility is 20% per annum, and the risk-free interest rate is 6% per annum. What is the value of a 5-month European put on the futures with a strike price of
Suppose that a futures price is currently 35. A European call option and a European put option on the futures with a strike price of 34 are both priced at 2 in the market. The risk-free interest rate
"The price of an at-the-money European call futures option always equals the price of a similar at-the-money European put futures option." Explain why this statement is true.AppendixLO1
Suppose that a futures price is currently 30. The risk-free interest rate is 5% per annum. A 3-month American call futures option with a strike price of 28 is worth 4. Calculate bounds for the price
Can an option on the yen/euro exchange rate be created from two options, one on the dollar/euro exchange rate, and the other on the dollar-yen exchange rate? Explain your answer.AppendixLO1
A corporation knows that in 3 months it will have $5 million to invest for 90 days at LIBOR minus 50 basis points and wishes to ensure that the rate obtained will be at least 6.5%. What position in
Prove the results in equations (14.1), (14.2), and (14.3) using the following portfolios: Portfolio A: one European call option plus an amount of cash equal to Ke-T Portfolio B: e shares, with
Show that, if C is the price of an American call with strike price K and maturity T on a stock providing a dividend yield of q, and P is the price of an American put on the same stock with the same
Show that, if C is the price of an American call option on a futures contract when the strike price is K and the maturity is T, and P is the price of an American put on the same futures contract with
If the price of currency A expressed in terms of the price of currency B follows the process dS=(BA)Sdt+oS dz where rA is the risk-free interest rate in currency A and B is the risk-free interest
Use the DerivaGem software to calculate implied volatilities for the March 104 call and the March 104 put on the Dow Jones Industrial Average (DJX) in Table 14.1. The value of the DJX on February 4,
A stock index currently stands at 300. It is expected to increase or decrease by 10% over each of the next two time periods of 3 months. The risk-free interest rate is 8% and the dividend yield on
Suppose that the spot price of the Canadian dollar is US S0.75 and that the Canadian dollar/US dollar exchange rate has a volatility of 4% per annum. The risk-free rates of interest in Canada and the
A mutual fund announces that the salaries of its fund managers will depend on the performance of the fund. If the fund loses money, the salaries will be zero. If the fund makes a profit, the salaries
A futures price is currently 40. It is known that at the end of 3 months the price will be either 35 or 45. What is the value of a 3-month European call option on the futures with a strike price of
Calculate the implied volatility of soybean futures prices from the following information concerning a European put on soybean futures: Current futures price 525 Exercise price 525 Risk-free rate 6%
Use the DerivaGem software to calculate implied volatilities for the July options on corn futures in Table AppendixLO1
Assume the futures prices in Table 2.2 apply and that the risk-free rate is 1.1% per annum. Treat the options as American and use 100 time steps. The options mature on June 19, 2004. Can you draw any
Explain how a stop-loss hedging scheme can be implemented for the writer of an out-of- the-money call option. Why does it provide a relatively poor hedge?AppendixLO1
What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of each option is 0.7?AppendixLO1
Calculate the delta of an at-the-money 6-month European call option on a non- dividend-paying stock when the risk-free interest rate is 10% per annum and the stock price volatility is 25% per
What does it mean to assert that the theta of an option position is -0.1 when time is measured in years? If a trader feels that neither a stock price nor its implied volatility will change, what type
Why did portfolio insurance not work well on October 19, 1987?AppendixLO1
The Black-Scholes price of an out-of-the-money call option with an exercise price of $40 is $4. A trader who has written the option plans to use a stop-loss strategy. The trader's plan is to buy at
Suppose that a stock price is currently $20 and that a call option with an exercise price of $25 is created synthetically using a continually changing position in the stock. Consider the following
What is the delta of a short position in 1,000 European call options on silver futures? The options mature in 8 months, and the futures contract underlying the option matures in 9 months. The current
In Problem 15.10, what initial position in 9-month silver futures is necessary for delta hedging? If silver itself is used, what is the initial position? If 1-year silver futures are used, what is
A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency. Which of the following would give the most favorable result? (a) A virtually constant spot
Repeat Problem 15.12 for a financial institution with a portfolio of short positions in put and call options on a currency.AppendixLO1
A financial institution has just sold 1,000- 7-month European call options on the Japanese yen. Suppose that the spot exchange rate is 0.80 cent per yen, the exercise price is 0.81 cent per yen, the
Under what circumstances is it possible to make a European option on a stock index both gamma neutral and vega neutral by adding a position in one other European option?AppendixLO1
A fund manager has a well-diversified portfolio that mirrors the performance of the S&P 500 and is worth $360 million. The value of the S&P 500 is 1,200, and the portfolio manager would like to buy
Repeat Problem 15.16 on the assumption that the portfolio has a beta of 1.5. Assume that the dividend yield on the portfolio is 4% per annum.AppendixLO1
Show by substituting for the various terms in equation (15.7) that the equation is true for: (a) A single European call option on a non-dividend-paying stock (b) A single European put option on a
What is the equation corresponding to equation (15.7) for (a) a portfolio of derivatives on a currency and (b) a portfolio of derivatives on a futures contract?AppendixLO1
Suppose that $70 billion of equity assets are the subject of portfolio insurance schemes. Assume that the schemes are designed to provide insurance against the value of the assets declining by more
Does a forward contract on a stock index have the same delta as the corresponding futures contract? Explain your answer.AppendixLO1
Use the put-call parity relationship to derive, for a non-dividend-paying stock, the relationship between: (a) The delta of a European call and the delta of a European put (b) The gamma of a European
Consider a 1-year European call option on a stock when the stock price is $30, the strike price is $30, the risk-free rate is 5%, and the volatility is 25% per annum. Use the DerivaGem software to
A financial institution has the following portfolio of over-the-counter options on sterling: Type Position Delta of option Gamma of option Vega of option Call -1,000 0.50 2.2 1.8 Call -500 0.80 0.6
Consider again the situation in Problem 15.25. Suppose that a second traded option with a delta of 0.1, a gamma of 0.5, and a vega of 0.6 is available. How could the portfolio be made delta, gamma,
A deposit instrument offered by a bank guarantees that investors will receive a return during a 6-month period that is the greater of (a) zero and (b) 40% of the return provided by a market index. An
The formula for the price c of a European call futures option in terms of the futures price Fo is given in Chapter 14 as where c=e[FoN(d)- KN(d)] d = = In(Fo/K)+0T/2 and dd-oT and K, r, T, and are
Use. Deriva Gem to check that equation (15.7) is satisfied for the option considered in Section 15.1. (Note: DerivaGem produces a value of theta "per calendar day". The theta in equation (15.7) is
Use the Deriva Gem Application Builder functions to reproduce Table 15.2. (In Table 15.2 the stock position is rounded to the nearest 100 shares.) Calculate the gamma and theta of the position each
An investor enters into a short forward contract to sell 100,000 British pounds for US dollars at an exchange rate of 1.5000 US dollars per pound. How much does the investor gain or lose if the
Suppose that you write a put contract with a strike price of $40 and an expiration date in 3 months. The current stock price is $41 and the contract is on 100 shares. What have you committed yourself
What is the difference between the over-the-counter market and the exchange-traded market? What are the bid and offer quotes of a market maker in the over-the-counter market?AppendixLO1
You would like to speculate on a rise in the price of a certain stock. The current stock price is $29, and a 3-month call with a strike price of $30 costs $2.90. You have $5,800 to invest. Identify
Suppose that you own 5,000 shares worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next 4 months?AppendixLO1
Explain why a forward contract can be used for either speculation or hedging.AppendixLO1
Suppose that a March call option to buy a share for $50 costs $2.50 and is held until March. Under what circumstances will the holder of the option make a profit? Under what circumstances will the
Suppose that a June put option to sell a share for $60 costs $4 and is held until June. Under what circumstances will the seller of the option (i.e., the party with the short position) make a profit?
It is May and a trader writes a September call option with a strike price of $20. The stock price is $18 and the option price is $2. Describe the trader's cash flows if the option is held until
A trader writes a December put option with a strike price of $30. The price of the option is $4. Under what circumstances does the trader make a gain?AppendixLO1
A company knows that it is due to receive a certain amount of a foreign currency in 4 months. What type of option contract is appropriate for hedging?AppendixLO1
A United States company expects to have to pay 1 million Canadian dollars in 6 months. Explain how the exchange rate risk can be hedged using (a) a forward contract and (b) an option.AppendixLO1
A trader enters into a short forward contract on 100 million yen. The forward exchange rate is $0.0080 per yen. How much does the trader gain or lose if the exchange rate at the end of the contract
The Chicago Board of Trade offers a futures contract on long-term Treasury bonds. Characterize the traders likely to use this contract.AppendixLO1
"Options and futures are zero-sum games." What do you think is meant by this statement?AppendixLO1
Describe the profit from the following portfolio: a long forward contract on an asset and a long European put option on the asset with the same maturity as the forward contract and a strike price
On July 1, 2005, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2006. On September 1, 2005, it enters into a forward contract to sell 10 million Japanese yen on
Suppose that sterling/USD spot and forward exchange rates are as follows: Spot 90-day forward 180-day forward 1.6080 1.6056 1.6018 What opportunities are open to an arbitrageur in the following
The price of gold is currently $500 per ounce. The forward price for delivery in 1 year is $700. An arbitrageur can borrow money at 10% per annum. What should the arbitrageur do? Assume that the cost
On May 29, 2003, an investor owns 100 Intel shares. As indicated in Table 1.2, the share price is $20.83 and an October put option with a strike price of $20 costs $1.50. The investor is comparing
Suppose that in the situation of Table 1.1 a corporate treasurer said: "I will have 1 million to sell in 6 months. If the exchange rate is less than 1.59, I want you to give me 1.59. If it is greater
Describe how foreign currency options can be used for hedging in the situation considered in Section 1.7 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.4600, and (b)
A trader buys a European call option and sells a European put option. The options have the same underlying asset, strike price, and maturity. Describe the trader's position. Under what circumstances
Distinguish between the terms open interest and trading volume."AppendixLO1
What is the difference between a local and a commission broker?AppendixLO1
Suppose that you enter into a short futures contract to sell July silver for $5.20 per ounce on the New York Commodity Exchange. The size of the contract is 5,000 ounces. The initial margin is
Suppose that in September 2006 you take a long position in a contract on May 2007 crude oil futures. You close out your position in March 2007. The futures price (per barrel) is $18.30 when you enter
What does a stop order to sell at $2 mean? When might it be used? What does a limit order to sell at $2 mean? When might it be used?AppendixLO1
What is the difference between the operation of the margin accounts administered by a clearinghouse and those administered by a broker?AppendixLO1
What differences exist in the way prices are quoted in the foreign exchange futures market, the foreign exchange spot market, and the foreign exchange forward market?AppendixLO1
The party with a short position in a futures contract sometimes has options as to the precise asset that will be delivered, where delivery will take place, when delivery will take place, and so on.
What are the most important aspects of the design of a new futures contract?AppendixLO1
Explain how margins protect investors against the possibility of default.AppendixLO1
An investor enters into two long July futures contracts on orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is
Show that if the futures price of a commodity is greater than the spot price during the delivery period than there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures
Explain the difference between a market-if-touched order and a stop order.AppendixLO1
Explain what a stop-limit order to sell at 20.30 with a limit of 20.10 means.AppendixLO1

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