Exotic Options Trading

Frans de Weert

• Publisher: Wiley
• Year: 2011
• Print ISBN: 9780470517901
• eBook ISBN: 9781119995180
• Edition: 1
• Topic: Business
• Subtopic: Finance
• Index: Business

Written by an experienced trader and consultant, Frans de Weert's Exotic Options Trading offers a risk-focused approach to the pricing of exotic options. By giving readers the necessary tools to understand exotic options, this book serves as a manual to equip the reader with the skills to price and risk manage the most common and the most complex exotic options.

De Weert begins by explaining the risks associated with trading an exotic option before dissecting these risks through a detailed analysis of the actual economics and Greeks rather than solely stating the mathematical formulae. The book limits the use of mathematics to explain exotic options from an economic and risk perspective by means of real life examples leading to a practical interpretation of the mathematical pricing formulae.

The book covers conventional options, digital options, barrier options, cliquets, quanto options, outperformance options and variance swaps, and explains difficult concepts in simple terms, with a practical approach that gives the reader a full understanding of every aspect of each exotic option. The book also discusses structured notes with exotic options embedded in them, such as reverse convertibles, callable and puttable reverse convertibles and autocallables and shows the rationale behind these structures and their associated risks.

For each exotic option, the author makes clear why there is an investor demand; explains where the risks lie and how this affects the actual pricing; shows how best to hedge any vega or gamma exposure embedded in the exotic option and discusses the skew exposure.

By explaining the practical implications for every exotic option and how it affects the price, in addition to the necessary mathematical derivations and tools for pricing exotic options, Exotic Options Trading removes the mystique surrounding exotic options in order to give the reader a full understanding of every aspect of each exotic option, creating a useable tool for dealing with exotic options in practice.

" Although exotic options are not a new subject in finance, the coverage traditionally afforded by many texts is either too high level or overly mathematical. De Weert's exceptional text fills this gap superbly. It is a rigorous treatment of a number of exotic structures and includes numerous examples to clearly illustrate the principles. What makes this book unique is that it manages to strike a fantastic balance between the theory and actual trading practice. Although it may be something of an overused phrase to describe this book as compulsory reading, I can assure any reader they will not be disappointed. "

—Neil Schofield, Training Consultant and author of Commodity Derivatives: Markets and Applications

"Exotic Options Trading does an excellent job in providing a succinct and exhaustive overview of exotic options. The real edge of this book is that it explains exotic options from a risk and economical perspective and provides a clear link to the actual profit and pricing formulae. In short, a must read for anyone who wants to get deep insights into exotic options and start trading them profitably. "

—Arturo Bignardi

1

Introduction

Exotic options are options for which payoffs at maturity cannot be replicated by a set of standard options. This is obviously a very broad definition and does not do justice to the full spectrum and complexity of exotic options. Typically, exotic options have a correlation component. Which means that their price depends on the correlation between two or more assets. To understand an exotic option one needs to know above all where the risks of this particular exotic option lie. In other words, for which spot price are the gamma and vega largest and at which point during the term of this option does it have the largest Greeks. Secondly, one needs to understand the dynamics of the risks. This means that one needs to know how the risks evolve over time and how these risks behave for a changing stock or basket price. The reason that one needs to understand the risks of an exotic option before actually pricing it is because the risks determine how an exotic option should be priced. Once it is known where the risks lie and the method for pricing it is determined, one finds that the actual pricing is typically nothing more than a Monte Carlo method. In other words, the price of an exotic option is generally based on simulating a large set of paths and subsequently dividing the sum of the payoffs by the total number of paths generated. The method for pricing an exotic option is very important as most exotic options can be priced by using a set of different exotic options and therefore saving a considerable amount of time. Also, sometimes one needs to conclude that the best way to price a specific exotic option is by estimating the price with a series of standard options, as this method better captures the risk involved with this exotic option. The digital option is a good example of that and will be discussed in Chapter 9.

Before any exotic option is discussed it is important to fully understand the interaction between gamma and theta. Although this book assumes an understanding of all the Greeks and how they interact, the following two sections give a brief summary of the Greeks and how the profit of an option depends on one of the Greeks, namely the gamma. A more detailed discussion of the Greeks and the profit related to them can be found in An Introduction to Options Trading, F. de Weert.

2

Conventional Options, Forwards and Greeks¹

This section is meant to give a quick run through of all the important aspects of options and to provide a sufficient theoretical grounding in regular options. This grounding enables the reader to enter into the more complex world of exotic options. Readers who already have a good working knowledge of conventional options, Greeks and forwards can skip this chapter. Nonetheless, even for more experienced option practitioners, this section can serve as a useful look-up guide for formulae of the different Greeks and more basic option characteristics.

2.1 CALL AND PUT OPTIONS AND FORWARDS

Call and put options on stocks have been traded on organised exchanges since 1973. However, options have been traded in one form or another for many more years. The most common types of options are the call option and the put option. A call option on a stock gives the buyer the right, but not the obligation, to buy a stock at a pre-specified price and at or before a pre-specified date. A put option gives the buyer the right, but not the obligation, to sell the stock at a pre-specified price and at or before a pre-specified date. The pre-specified price at which the option holder can buy in the case of a call and sell in the case of a put is called the strike price. The buyer is said to exercise his option when he uses his right to buy the underlying share in case of a call option and when he sells the underlying share in case of a put option. The date at or up to which the buyer is allowed to exercise his option is called the maturity date or expiration date. There are two different terms regarding the timing of the right to exercise an option. They are identified by a naming convention difference. The first type is the European option where the option can only be exercised at maturity. The second type of option is the American option where the option can be exercised at any time up to and including the expiry date.

Figure 2.1 Payoff profile at maturity for a call option with strike price K

Obviously, the buyer of a European call option would only exercise his right to buy the underlying stock if the share price was higher than the strike price. In this case, the buyer can buy the share for the predetermined strike price by exercising the call and subsequently sell it in the market at the prevailing price in the market, which is higher than the strike price and therefore making a profit. The payoff profile of the call option is shown in Figure 2.1. The buyer of a European put option acts opposite to the buyer of the call option in the sense that the buyer of a put option would only exercise his option right, at maturity, if the share price was below the strike price. In this case the option buyer can first buy the share in the market at the prevailing market price and subsequently sell it at the strike price by exercising his put option, earning a profit as a result. The payoff profile at maturity of a put option is shown in Figure 2.2.

A forward is different to an option in the sense that the buyer of the forward is obliged to buy the stock at a pre-specified price and at a pre-specified date in the future. The pre-specified price of a forward is chosen in such a way that the price of the forward is zero at inception of the contract. Therefore, the expected fair value of the stock at a certain maturity date is often referred to as the forward value of a stock or simply the forward associated with the specific maturity. The payoff profile at maturity of a forward contract is shown in Figure 2.3. Figure 2.3 makes clear that there is a downside in owning a forward. Whereas the owner of an option always has a payout at maturity which is larger than zero and therefore the maximum loss is equal to the premium paid for the option, the maximum loss on one forward is equal to the strike price of the forward, which occurs if the share price goes to zero. Since the definition of a forward prescribes that the contract is worth zero at inception, the strike price of the forward is equal to the forward value, which is discussed more elaborately in sub-section 2.4.

Figure 2.2 Payoff profile at maturity for a put option with strike price K

Figure 2.3 Payoff profile at maturity for a forward with strike price K which is equal to the fair forward value

2.2 PRICING CALLS AND PUTS

In 1973 Black and Scholes introduced their famous Black-Scholes formula. The Black-Scholes formula makes it possible to price a call or a put option in terms of the following inputs:

• The underlying share price, S_t;

• The strike pr...

Table of contents

• Title Page
• Copyright Page
• Preface
• Acknowledgements
• Chapter 1 - Introduction
• Chapter 2 - Conventional Options, Forwards and Greeks
• Chapter 3 - Profit on Gamma and Relation to Theta
• Chapter 4 - Delta Cash and Gamma Cash
• Chapter 5 - Skew
• Chapter 6 - Simple Option Strategies
• Chapter 7 - Monte Carlo Processes
• Chapter 8 - Chooser Option
• Chapter 9 - Digital Options
• Chapter 10 - Barrier Options
• Chapter 11 - Forward Starting Options
• Chapter 12 - Ladder Options
• Chapter 13 - Lookback Options
• Chapter 14 - Cliquets
• Chapter 15 - Reverse Convertibles
• Chapter 16 - Autocallables
• Chapter 17 - Callable and Puttable Reverse Convertibles
• Chapter 18 - Asian Options
• Chapter 19 - Quanto Options
• Chapter 20 - Composite Options
• Chapter 21 - Outperformance Options
• Chapter 22 - Best of and Worst of Options
• Chapter 23 - Variance Swaps
• Chapter 24 - Dispersion
• Chapter 25 - Engineering Financial Structures
• Appendix A - Variance of a Composite Option and Outperformance Option
• Appendix B - Replicating the Variance Swap
• Bibliography
• Index