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You have successfully signed out and will be required to sign back in should you need to download more resources. Options, Futures, and Other Derivatives, 10th Edition. John C. Hull, University of Toronto. How frequently would the balance in the account of a client with a long position be negative immediately before a margin payment is due so that the client has an incentive to default? Assume that balances in excess of the initial margin are withdrawn by the client. This suggests that price changes have heavier tails than the normal distribution.
In July , a small chocolate factory receives a large order for chocolate bars to be delivered in November. It will need 10 metric tons of Cocoa in September to fill this order. For each alternative, what is: a the upfront cost? Ten trading days later, the futures price of the index drops to 1, triggering a margin call for the trader. What is the change margin account balance indicate gain or loss for: a the trader and b the hedge fund? What is the margin call for the trader? A speculator sells a July wheat futures contract at cents per bushel.
Each futures contract is for 5, bushels. The futures price drops to on December 31, and rises to in May when she closes the contract. What is the gain or loss for accounting purposes in ? In December , a company expects to buy , MMBtu of natural gas before the end of March , but does not know exactly when. To hedge against volatile gas prices, it implements a rolling forward hedge by taking a long position on 10 twomonth natural gas futures only held for 1 month. The commodity is purchased in March Assume a hedge ratio of 0.
A trader owns 55, troy oz of silver and decides to hedge with 6-month silver futures contracts. Each futures contract is on 5, troy oz. The standard deviation of the change in the spot price of silver is 0. The standard deviation of the change in silver futures prices is 0. The coefficient of correlation between the two is 0. What is the minimum variance hedge ratio? What is the optimal number of futures contracts without tailing the hedge?
What is the optimal number of futures contracts with tailing the hedge? Semi-annually b. Quarterly c. Monthly d. Weekly e. Daily 9. Given the zero rates and cash flows for a bond see table below : a. What is the theoretical price?
What is the bond yield? A stock provides a dividend yield of 5. What is the two-year forward price for a stock? What is the continuously compounded cost of carry for the stock? A US investor sees an arbitrage opportunity in the currency markets.
Assume the continuously compounded interest rates in the US and Switzerland are 0. The 3-month currency forward price is 1. What is the theoretically correct forward price? Consider a currency swap with 3 years remaining. A financial institution receives 3. The British rate is 2. By valuing the currency swap as fixed-rate bonds, what is: a.
An investor buys 5 call option contracts, each on shares with a strike of There is a 6-for-5 stock split. Give the following: a. The new strike price 50 b. The new number of shares underlying the 5 contracts What is the implied risk-free interest rate? Note: Total payoff does not include initial investment a. What is the initial investment? What is the total payoff when the stock price in 9 months is ?
A 1-year option is offered on a non-dividend-paying stock. When the Black-ScholesMerton model is used a. What is the value of d1? What is the value of d2? What is the price of a call option, c? What is the price of a put option, p? What is the present value of the dividends? Discuss the pros and cons of executive stock options versus paying executives directly with stock. However, this overlooks the asymmetric payoffs of options. If the company does badly then the shareholders lose money, but all that happens to the executives is that they fail to make a gain.
Unlike the shareholders, they do not experience a loss. Many people think that a better type of pay for performance is a restricted stock unit. The gains and losses of the executives then mirror those of other shareholders. It is sometimes argued that the asymmetric payoffs of options can lead top senior executives taking risks they would not otherwise take.
A two-step binomial tree is used to value an option on the Australian dollar. The strike price is 1. Each step is 3 months. The current price of one AUD is 1. The US risk free rate is 2. What is the proportional up movement, u, for the currency? What is the probability of an up movement, p? What is the price of an American call option on the currency? The spot price of an index is A trader decides to hedge her portfolio against large market moves by taking positions in the underlying asset and two options see table below.
How many units of options 1 and 2, respectively, are needed to make the portfolio gamma and vega neutral? How many units of the underlying asset are needed to make the hedged. A trader decides to protect her portfolio with a put option. Because the option is not available on exchanges, the trader decides to create an option by maintaining a position in the underlying portfolio with the required delta. What percentage of the original portfolio should be sold and invested at the risk-free rate: a.
Initially at time zero? What is the probability of an up move? These notes make some suggestions on the teaching of the chapters and mention some of the differences between the 9th and 10th editions.
Instructors should be aware that solutions to end-of chapter problems in all textbooks in all subjects tend to have found their way to the web. This textbook is unfortunately no exception. I have found that very few of my students search the web for solutions to problems, but other instructors tell me that they regard this as a serious issue. For these I provide only the answers, not how they are derived.
Even if a student finds the answer on the web, s he still has to work out where it comes from. CHAPTER 1 Introduction This chapter introduces the markets for futures, forward, and option contracts and explains the activities of hedgers, speculators, and arbitrageurs. Issues concerning futures contracts such as margin requirements, settlement procedures, the role of the clearinghouse, etc are covered in Chapter 2.
Some instructors prefer to avoid any mention of options until the material on linear products in Chapters 1 to 7 has been covered. I like to introduce students to options in the first class, even though they are not mentioned again for several classes.
This is because most students find options to be the most interesting of the derivatives covered and I like students to be enthusiastic about the course early on. The way in which the material in Chapter 1 is covered is likely to depend on the backgrounds of the students.
If a course in investments is a prerequisite, Chapter 1 can be regarded as a review of material already familiar to the students and can be covered fairly quickly. If an investments course is not a prerequisite, more time may be required.
Increasingly, some aspects of derivatives markets are being covered in introductory corporate finance courses, accounting courses, strategy courses, etc. In many instances students are, therefore, likely to have had some exposure to the material in Chapter 1. I do not require an investments elective as a prerequisite for my elective on futures and options markets and find that 1 12 to 2 hours is necessary for me to introduce the course and cover the material in Chapter 1.
To motivate students at the outset of the course, I discuss the growing importance of derivatives, how much experts in the field are paid, etc. It is not uncommon for students. I defer a discussion of the crisis until the Chapter 8 material is covered. Towards the end of the first class I usually produce a current newspaper and describe several traded futures and options.
I then ask students to guess the quoted price. Sometimes votes are taken. This is an enjoyable exercise and forces students to think actively about the nature of the contracts and the determinants of price. It usually leads to a preliminary discussion of such issues as the relationship between a futures price and the corresponding spot price, the desirability of options being exercised early, why most options sell for more than their intrinsic value, etc.
While covering the Chapter 1 material, I treat futures as the same as forwards for the purposes of discussion. I try to avoid being drawn into a discussion of such issues as the mechanics of futures, margin requirements, daily settlement procedures, and so on until I am ready.
These topics are covered in Chapter 2. As will be evident from the slides that go with this chapter, I usually introduce students to a little of the Chapter 5 material during the first class. I discuss how arbitrage arguments tie the futures price of gold to its spot price and why the futures price of a consumption commodity such as oil is not tied to its spot price in the same way.
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