CHAPTER 1
Foreign Exchange Derivatives

The FX derivatives market consists of FX swaps, FX forwards, FX or currency options, and other more general derivatives. FX structured products are either standardized or tailor-made linear combinations of simple FX derivatives including both vanilla and exotic options, or more general structured derivatives that cannot be decomposed into simple building blocks. The market for structured products is restricted to the market of the necessary ingredients. Hence, typically there are mostly structured products traded in the currency pairs that can be formed between USD, JPY, EUR, CHF, GBP, CAD and AUD. In this chapter we start with a brief history of options, followed by a technical section on vanilla options and volatility, and deal with commonly used linear combinations of vanilla options. Then we will illustrate the most important ingredients for FX structured products: the first and second generation exotics.

1.1 LITERATURE REVIEW

While there are tons of books on options and derivatives in general, very few are dedicated specifically to FX options. After the 2008 financial crisis, more such books appeared. Shamah [118] is a good source to learn about FX markets with a focus on market conventions, spot, forward, and swap contracts, and vanilla options. For pricing and modeling of exotic FX options I (obviously) suggest Hakala and Wystup's Foreign Exchange Risk [65] or its translation into Mandarin [68] as useful companions to this book. One of the first books dedicated to Mathematical Models for Foreign Exchange is by Lipton [92]. In 2010, Iain Clark published Foreign Exchange Option Pricing [28], and Antonio Castagna one on FX Options and Smile Risk [25], which both make a valuable contribution to the FX derivatives literature. A classic is Alan Hicks's Managing Currency Risk Using Foreign Exchange Options [76]. It provides a good overview of FX options mainly from the corporate's point of view. An introductory book on Options on Foreign Exchange is by DeRosa [38]. The Handbook of Exchange Rates [82] provides a comprehensive compilation of articles on the FX market structure, products, policies, and economic models.

1.2 A JOURNEY THROUGH THE HISTORY OF OPTIONS

The very first options and futures were traded in ancient Greece, when olives were sold before they had reached ripeness. Thereafter the market evolved in the following way.

• 16th century Ever since the 15th century, tulips, which were desired for their exotic appearance, were grown in Turkey. The head of the royal medical gardens in Vienna, Austria, was the first to cultivate those Turkish tulips successfully in Europe. When he fled to Holland because of religious persecution, he took the bulbs along. As the new head of the botanical gardens of Leiden, Netherlands, he cultivated several new strains. It was from these gardens that avaricious traders stole the bulbs to commercialize them, because tulips were a great status symbol.
• 17th century The first futures on tulips were traded in 1630. As of 1634, people could buy special tulip strains by the weight of their bulbs - the bulbs had the same value as gold. Along with the regular trading, speculators entered the market and the prices skyrocketed. A bulb of the strain, "Semper Octavian," was worth two wagonloads of wheat, four loads of rye, four fat oxen, eight fat swine, twelve fat sheep, two hogsheads of wine, four barrels of beer, two barrels of butter, 1,000 pounds of cheese, one marriage bed with linen, and one sizable wagon. People left their families, sold all their belongings, and even borrowed money to become tulip traders. When in 1637 this supposedly risk-free market crashed, traders as well as private individuals went bankrupt. The Dutch government prohibited speculative trading; the period became famous as Tulipmania.
• 18th century In 1728, the West India and Guinea Company, the monopolist in trading with the Caribbean Islands and the African coast, issued the first stock options. These were options on the purchase of the French island of Sainte-Croix, on which sugar plantings were planned. The project was realized in 1733 and paper stocks were issued in 1734. Along with the stock, people purchased a relative share of the island and the valuables, as well as the privileges and the rights of the company.
• 19th century In 1848, 82 businessmen founded the Chicago Board of Trade (CBOT). Today it is the biggest and oldest futures market in the entire world. Most written documents were lost in the great fire of 1871; however, it is commonly believed that the first standardized futures were traded as of 1860. CBOT now trades several futures and forwards, not only treasury bonds but also options and gold. In 1870, the New York Cotton Exchange was founded. In 1880, the gold standard was introduced.
• 20th century
  • In 1914, the gold standard was abandoned because of the First World War.
  • In 1919, the Chicago Produce Exchange, in charge of trading agricultural products, was renamed the Chicago Mercantile Exchange. Today it is the most important futures market for the Eurodollar, foreign exchange, and livestock.
  • In 1944, the Bretton Woods System was implemented in an attempt to stabilize the currency system.
  • In 1970, the Bretton Woods System was abandoned for several reasons.
  • In 1971, the Smithsonian Agreement on fixed exchange rates was introduced.
  • In 1972, the International Monetary Market (IMM) traded futures on coins, currencies and precious metal.
  • In 1973, the CBOE (Chicago Board of Exchange) firstly traded call options; four years later it added put options. The Smithsonian Agreement was abandoned; the currencies followed managed floating.
  • In 1975, the CBOT sold the first interest rate future, the first future with no "real" underlying asset.
  • In 1978, the Dutch stock market traded the first standardized financial derivatives.
  • In 1979, the European Currency System was implemented, and the European Currency Unit (ECU) was introduced.
  • In 1991, the Maastricht Treaty on a common currency and economic policy in Europe was signed.
  • In 1999, the Euro was introduced, but the countries still used cash of their old currencies, while the exchange rates were kept fixed.
• 21st century In 2002, the Euro was introduced as new money in the form of cash.

FX forwards and options originate from the need of corporate treasury to hedge currency risk. This is the key to understanding FX options. Originally, FX options were not speculative products but hedging products. This is why they trade over the counter (OTC). They are tailored, i.e. cash flow matching currency risk hedging instruments for corporates. The way to think about an option is that a corporate treasurer in the EUR zone has income in USD and needs a hedge to sell the USD and to buy EUR for these USD. He would go long a forward or a EUR call option. At maturity he would exercise the option if it is in-the-money and receive EUR and pay USD. FX options are by default delivery settled. While FX derivatives were used later also as investment products or speculative instruments, the key to understanding FX options is corporate treasury.

1.3 CURRENCY OPTIONS

Let us start with a definition of a currency option:

Definition 1.3.1   A Currency Option Transaction means a transaction entitling the Buyer, upon Exercise, to purchase from the Seller at the Strike Price a specified quantity of Call Currency and to sell to the Seller at the Strike Price a specified quantity of Put Currency.

This is the definition taken from the 1998 FX and Currency Option Definitions published by the International Swaps and Derivatives Association (ISDA) in 1998 [77]. This definition was the result of a process of standardization of currency options in the industry and is now widely accepted. Note that the key feature of an option is that the holder has a right to exercise. The definition also demonstrates clearly that calls and puts are equivalent, i.e. a call on one currency is always a put on the other currency. The definition is designed for a treasurer, where an actual cash flow of two currencies is triggered upon exercise. The definition also shows that the terms derivative and option are not synonyms. Derivative is a much wider term for financial transactions that depend on an underlying traded instrument. Derivatives include forwards, swaps, options, and exotic options. But not any derivative is also an option. For a currency option there is always a holder, the buyer after buying the option, equipped with the right to exercise, and upon exercise a cash flow of two pre-specified currencies is triggered. Anything outside this definition does not constitute a currency option. I highly recommend reading the 1998 ISDA definitions. The text uses legal language, but it does make all the terms around FX and currency options very clear and it is the benchmark in the industry. It covers only put and call options, options that are typically referred to as vanilla options, because they are the most common and simple products. The definition allows for different exercise styles: European for exercise permitted only at maturity, American for exercise permitted at any time between inception and maturity, as well as Bermudan for exercise permitted as finitely many pre-specified points...