An Introduction to Options Trading E-Book

Frans de Weert

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Securities and Investment Institute
• Sprache: Englisch

Seitenzahl: 160

Veröffentlichungsjahr: 2011

Beschreibung

Explaining the theory and practice of options from scratch, this book focuses on the practical side of options trading, and deals with hedging of options and how options traders earn money by doing so. Common terms in option theory are explained and readers are shown how they relate to profit. The book gives the necessary tools to deal with options in practice and it includes mathematical formulae to lift explanations from a superficial level. Throughout the book real-life examples will illustrate why investors use option structures to satisfy their needs.

Leseprobe

Table of Contents

The Securities & Investment Institute

Title Page

Copyright Page

Dedication

PREFACE

Acknowledgements

Introduction

Chapter 1 - OPTIONS

1.1 EXAMPLES

1.2 AMERICAN VERSUS EUROPEAN OPTIONS

1.3 TERMINOLOGY

1.4 EARLY EXERCISE OF AMERICAN OPTIONS

1.5 PAYOFFS

1.6 PUT-CALL PARITY

Chapter 2 - THE BLACK – SCHOLES FORMULA

2.1 VOLATILITY AND THE BLACK-SCHOLES FORMULA

2.2 INTEREST RATE AND THE BLACK-SCHOLES FORMULA

2.3 PRICING AMERICAN OPTIONS

Chapter 3 - DIVIDENDS AND THEIR EFFECT ON OPTIONS

3.1 FORWARDS

3.2 PRICING OF STOCK OPTIONS INCLUDING DIVIDENDS

3.3 PRICING OPTIONS IN TERMS OF THE FORWARD

3.4 DIVIDEND RISK FOR OPTIONS

3.5 SYNTHETICS

Chapter 4 - IMPLIED VOLATILITY

4.1 EXAMPLE

4.2 STRATEGY AND IMPLIED VOLATILITY

Chapter 5 - DELTA

5.1 DELTA-HEDGING

5.2 THE MOST DIVIDEND-SENSITIVE OPTIONS

5.3 EXERCISE-READY AMERICAN CALLS ON DIVIDEND PAYING STOCKS

Chapter 6 - THREE OTHER GREEKS

6.1 GAMMA

6.2 THETA

6.3 VEGA

Chapter 7 - THE PROFIT OF OPTION TRADERS

7.1 DYNAMIC HEDGING OF A LONG CALL OPTION

7.2 DYNAMIC HEDGING OF A SHORT CALL OPTION

7.3 PROFIT FORMULA FOR DYNAMIC HEDGING

7.4 THE RELATIONSHIP BETWEEN DYNAMIC HEDGING AND θ

7.5 THE RELATIONSHIP BETWEEN DYNAMIC HEDGING AND θ WHEN THE INTEREST RATE IS ...

7.6 CONCLUSION

Chapter 8 - OPTION GREEKS IN PRACTICE

8.1 INTERACTION BETWEEN GAMMA AND VEGA

8.2 THE IMPORTANCE OF THE DIRECTION OF THE UNDERLYING SHARE TO THE OPTION GREEKS

8.3 PIN RISK FOR SHORT-DATED OPTIONS

8.4 THE RISKIEST OPTIONS TO GO SHORT

Chapter 9 - SKEW

9.1 WHAT IS SKEW?

9.2 REASONS FOR SKEW

9.3 REASONS FOR HIGHER VOLATILITIES IN FALLING MARKETS

Chapter 10 - SEVERAL OPTION STRATEGIES

10.1 CALL SPREAD

10.2 PUT SPREAD

10.3 COLLAR

10.4 STRADDLE

10.5 STRANGLE

Chapter 11 - DIFFERENT OPTION STRATEGIES AND WHY INVESTORS EXECUTE THEM

11.1 THE PORTFOLIO MANAGER’S APPROACH TO OPTIONS

11.2 OPTIONS AND CORPORATES WITH CROSS-HOLDINGS

11.3 OPTIONS IN THE EVENT OF A TAKEOVER

11.4 RISK REVERSALS FOR INSURANCE COMPANIES

11.5 PRE-PAID FORWARDS

11.6 EMPLOYEE INCENTIVE SCHEMES

11.7 SHARE BUY-BACKS

Chapter 12 - TWO EXOTIC OPTIONS

12.1 THE QUANTO OPTION

12.2 THE COMPOSITE OPTION

Chapter 13 - REPO

13.1 A REPO EXAMPLE

13.2 REPO IN CASE OF A TAKEOVER

13.3 REPO AND ITS EFFECT ON OPTIONS

13.4 TAKEOVER IN CASH AND ITS EFFECT ON THE FORWARD

Appendix A - PROBABILITY THAT AN OPTION EXPIRES IN THE MONEY

Appendix B - VARIANCE OF A COMPOSITE OPTION

BIBLIOGRAPHY

INDEX

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To Jan and Annelies

PREFACE

This book is appropriate for people who want to get a good overview of options in practice. It especially deals with hedging of options and how option traders earn money by doing so. To point out where the profit of option traders comes from, common terms in option theory will be explained, and it is shown how they relate to this profit. The use of mathematics is restricted to a minimum. However, since mathematics makes it possible to lift analyses to a non-superficial level, mathematics is used to clarify and generalize certain phenomena.

The aim of this book is to give both option practitioners as well as interested individuals the necessary tools to deal with options in practice. Throughout this book real life examples will illustrate why investors use option structures to satisfy their needs. Although understanding the contents of this book is a prerequisite for becoming a good option practitioner, a book can never produce a good trader. Ninety percent of a trader’s job is about dealing with severe losses and still being able to make the right decisions if such a loss occurs. The only way to become a good trader is to accept that, when helping clients to execute their option strategies, the trader will inevitably end up with positions where the risk reward is against him but the odds are in his favour. For that reason a one-off loss will almost always be larger than a one-off gain. But, if a trader executes many deals he should be able to make money on the small margin he collects on every deal even if he gets a few blow-ups.

ACKNOWLEDGEMENTS

This book is based on knowledge acquired during my work as a trader at Barclays Capital. Therefore, I would like to thank my colleagues at Barclays Capital who have been very helpful in teaching me the theory and practice of options. At Barclays Capital I would especially like to thank Faisal Khan and Thierry Lucas for giving me all the opportunities to succeed in mastering and practising option trading. I would also like to thank Thierry Lucas for his many suggestions and corrections when reviewing my work and Alex Boer for his mathematical insights. I would especially like to thank Karma Dajani for first giving me a great foundation in probability theory, then supervising my graduate dissertation in mathematics and, lastly, reviewing this book. Special thanks goes out to my father, Jan de Weert, for having been a motivating and helpful force in mastering mathematics throughout my life, and for checking the book very thoroughly and giving me many suggestions in rephrasing sentences and formulae more clearly.

INTRODUCTION

Over the years derivative securities have become increasingly important. Examples of these are options, futures, forwards and swaps. Although every derivative has its own purpose, they all have in common that their values depend on more basic variables like stocks and interest rates. This book is only concerned with options, but once the theory behind options is known, knowledge can easily be expanded to other derivatives.

This book has three objectives. The first is to introduce terms commonly used in option theory and explain their practical interpretation. The second is to show where option traders get their profit and how these commonly used terms relate to this profit. The last objective is to show why companies and investors use options to satisfy their financial needs.

Chapter 1

OPTIONS

Options on stocks were first traded on an organized exchange in 1973. That very same year Black and Scholes introduced their famous Black-Scholes formula. This formula gives the price of an option in terms of its parameters, like the underlying asset, time to maturity and interest rate. The formula and the variables it depends on will be discussed in more detail in the next chapters. Since 1973 option markets have grown rapidly, not only in volumes but also in the range of option products to be traded. Nowadays, options can be traded on many different exchanges throughout the world and on many different underlying assets. These underlying assets include stocks, stock indices, currencies and commodities.

There are two general kinds of options, the call option and the putoption. A call option gives the holder the right, but not the obligation, to buy the underlying asset for a pre-specified price and at a pre-specified date. A put option gives the holder the right, but not the obligation, to sell the underlying asset for a pre-specified price and at a pre-specified date. This pre-specified price is called the ‘strike price’; the date is known as the ’expiration date’, or ‘maturity’. The underlying asset in the definition of an option can be virtually anything, like potatoes, the weather, or stocks. Throughout this book the underlying asset will be taken to be a stock.

When the owner of a call option chooses to buy the stock, it is said that he exercises his option right. Of course, the same holds for the owner of a put option, only in this case the owner chooses to sell the stock, but it is still referred to as ‘exercising’ the option. If the option can only be exercised on the expiration date itself, the option is said to be a ‘European’ option. If it can be exercised at any time up to expiration, the option is an ‘American’ option. Although there are many other option types, the most important ones have already been covered: American call option, American put option, European call option and the European put option. The vast majority of the options that are traded on exchanges are American. However, it is useful to analyze European options, because properties of American options can very often be deduced from its European counterpart.

Before an example is given, it is worthwhile to look at the boldface sentence in the definition of an option. The holder of an option is not obligated to exercise the option. This means that at maturity the holder can decide not to do anything. This is exactly why it is called an ‘option’, the holder has a choice of doing something. Because of this choice, the largest loss an owner of an option can face is the price paid for the option.

1.1 EXAMPLES

Consider a holder of a European call option on the stock Royal Dutch/Shell with a strike price of $42. Suppose that the current stock price is $40, the expiration date is in 1 year and the option price is $5. Since the option is European, it can only be exercised on the expiration date. What are the possible payoffs for this option? If on the expiration date the stock price is less than $42, the holder of this option will clearly not exercise his option right. For if he did, he would buy the stock for $42 (exercising the option), and would only be able to sell the stock on the market for less than $42. So, the holder would incur a loss if he exercised his right, whereas nothing would happen if he did not exercise this right. In conclusion, if on the expiration date the stock price is less than $42, the holder does not exercise the option. In these circumstances the holder’s loss is the price paid for the option, in this case $5. If on the expiration date the stock price is between $42 and $47, the holder will exercise his option right. Suppose that the stock price on the expiration date is $45, then, by exercising his option right, he buys the stock for $42 and immediately sells this stock on the market for $45, making a profit of $3. However, taking into account that he paid $5 for the option, he still makes a loss of $2. It is clear that up to $47 the holder loses money on the option. If on the expiration date the stock price is more than $47, the holder will again exercise his option right. The difference between this case and the previous one is that the holder not only makes a profit by exercising his option right, he also makes an overall profit. Suppose that the stock price on the expiration date is $49, then his profit is $2, $7 from exercising the option and – $5 from the price paid for the option. Figure 1.1 shows the way in which the profit of the holder of a call option on Royal Dutch/Shell varies with the stock price at maturity.

This example points out that the profit of the holder of a call option increases as the stock price increases. Thus, the holder of a call option is speculating on an increasing stock price.

In contrast to a call option, the owner of a put option is hoping that the stock price will decrease. Consider a holder of a European put option on Unilever with a strike price of $50. Suppose that the current stock price is $50, the expiration date is in 6 months and the option price is $3. Again, because the put option is European it can only be exercised on the expiration date. What are the possible payoffs for the put option? Suppose that the stock price at maturity (expiration date) is more than $50. In this case the holder would not exercise his option right. Because he would have to buy the stock for more than $50, and, under the conditions of the put options, sell the same stock for $50. This would mean he would always incur a loss. So, if the stock price is more than $50, the holder does not exercise the option and faces a loss of $3, the price paid for the put option. If the stock price at maturity is between $50 and $47, the holder will exercise the option, but still make an overall loss. He will earn money by exercising the option, but it will not be enough to make up for the initial $3 paid for the option. If the stock price is less than $47 at maturity, the holder will exercise the option, and make an overall profit. He will make a profit of more than $3 by buying the stock on the market and immediately selling this stock for $50 under the conditions of the put option. Since the price paid for the put option was $3 he will also make an overall profit. Figure 1.2 shows the way in which the profit of the holder of the put option on Unilever varies with the stock price at maturity.

1.2 AMERICAN VERSUS EUROPEAN OPTIONS

If in above examples the options were American rather than European, the holders of the options would not have to wait until the expiration date before exercising the options. In the example of the put option on Unilever with strike price $50 this would mean that at any time during the 6 months, the holder is allowed to exercise the option. So, suppose that after 3 months the stock price is $40, the holder could decide to exercise his option right. By exercising he would make a profit of $7, $10 from exercising the option and – $3 from the price paid for the option.

Everything that can be done with a European option can be done with an American option, but the American option has the additional property that it can be exercised at any time up to the expiration date. This means that its price is always at least as much as its European counterpart.

Although most options that are traded on exchanges are American, this book mainly focuses on European options. Since American options are based on the same principles as European ones, and their properties can, very often, be easily derived from the European counterparts this is perfectly arguable. Throughout this book, an option is assumed to be European, unless specifically stated otherwise.

1.3 TERMINOLOGY

An option contract is an agreement between two parties. The buyer of the option is said to ‘have taken a long position’ in the option. The other party is said to have taken a ‘short position’ in the option, or is said to have ‘written’ the option. So, taking a long position essentially means ‘buying’ and taking a short position means ‘selling’. For that reason there are four general option positions:

1. A short position in a call option.

2. A short position in a put option.

3. A long position in a call option.

4. A long position in a put option.