Investing in Exotic Options

Kevin Cheng

15.1 Chapter Introduction and Objectives

In Chap. 14, we introduced the pricing of plain vanilla call and put options on dividend paying and nondividend paying stocks. In this chapter we introduce the pricing of "exotic options." This chapter has the following objectives:

• Introduce different types of exotic options

• Discuss the pricing of Barrier, Look back, Binary, Asian, and spread options

Exotic options are a class of derivative products, which allow the buyer (or seller) of the option to capture return profiles, which are more specific to their expectations or needs. Compared to plain vanilla options and stocks, exotics can have additional features or characteristics that make them more attractive in terms of both risk and reward.

Although the options market has existed for hundreds of years, it was not until the late 1970s when the Black-Scholes model (Black and Scholes 1973) was published that practitioners began to trade more extensively in derivatives. Exotic equity options began trading soon after but gained much less interest through most of the 1970s, and vanilla options and warrants were the main products traded in the markets. It was not until the 1980s and, subsequently, the introduction of over-the-counter (OTC) markets in the 1990s that interest in exotic options picked up as investors sought new ways to generate returns and help to reduce risk in portfolios.

Even though interest in options has increased, the growth of options and derivatives, particularly during the 1990s, has been held back by the portrayal of derivatives as dangerous instruments, largely due to an association with large trading losses in recent history. A number of these cases stand out: Metallgesellschaft AG's losses in oil derivatives in late 1993, the collapse of Long-Term Capital Management in 1994, Enron's bankruptcy in 2001, and, more recently, the collapse of hedge

K. Cheng

Parallax Capital Management, 1 George Street, Singapore 49145, Singapore e-mail: [email protected]

S.R. Vishwanath, C. Krishnamurti (eds.), Investment Management: A Modern Guide 359

to Security Analysis and Stock Selection, DOI: 10.1007/978-3-540-88802-4.15, (c 2GG9 Springer-Verlag Berlin Heidelberg

Exhibit 15.1 Definition of notations

S Underlying asset price

X Strike price r Risk free rate

D Dividend yield a Volatility

T Time to maturity fund Amaranth Advisors LLC after losses exceeding US $6 billion. In most of these cases, the losses can be attributed to excessive leverage, improper risk management controls, and a general lack of understanding of these products. Nonetheless, the market for derivative products continues to grow at a phenomenal rate, leading to a demand from a wider range of investor classes, which in turn has led to the greater need for transparency and knowledge of both vanilla and exotic-type contracts.

This chapter introduces some of the concepts behind exotic options and their practical uses. Exhibit 15.1 defines the standard notation used throughout.

15.2 Exchange Traded vs. Over-the-Counter Market

Exchange-traded contracts refer to instruments that are traded on an exchange such as the London Stock Exchange (LSE) or the Chicago Board Options Exchange (CBOE). The contract specifications for exchange-traded options are standardized with respect to the number of underlying shares, tick size, and strikes, for example; thereby, providing a defined market place for option investors. Options which are exchange traded are primarily standard vanilla options on single stocks, America Depository Receipts (ADRs),1 or stock indices. Only a small percentage of these options are considered exotic in nature.

The origins of option trading began thousands of years ago, but the trading of tulip options in the sixteenth century during the Dutch tulip bulb craze is often considered the first time option contracts been extensively traded. Fast forward to 1973 when vanilla options first traded on the Chicago Board of Trade (CBOT), the same year the Black and Scholes option pricing formula was announced. It was not until almost 20 years later that exchange-traded exotic options were first introduced on the CBOE in the early 1990s, followed shortly by the American Stock Exchange (AMEX), and, subsequently, brought onto other exchanges around the world. For example, S&P ASX 200 barrier options are traded on the Australian Stock Exchange (ASX). An extensive range of exotic derivatives on equities are also found on the Hong Kong Exchange (HKEX), the Stuttgart Stock Exchange (EUWAX), and the Scoach Schweiz AG [joint venture between the Swiss Exchange (SWX) and the Deutsche Borse (DBG)].

1 American Depository Receipts are issued by foreign companies on US exchanges.

Exhibit 15.2 Proportion of total over-the-counter (OTC) options market by asset class

Source: BIS Quarterly Review

When compared to other asset classes, such as interest rate and foreign exchange, exotic equity derivatives still make up only a small proportion of all derivative contracts traded; the vast majority of which are traded "OTC." The OTC market provides a marketplace for one counterparty to trade directly with another, usually between investment banks or between the banks and their clients.

Exhibit 15.2 illustrates the relative market size of each asset class based on notional amounts outstanding as of December 2006. Looking at the percentage may not give a clear picture, but when we consider that the total size of the global derivatives market is in excess of US $400 trillion per year, even a small slice of the pie is significant.

The advent of an OTC market has led to the phenomenal growth in the OTC options traded. The Bank of International Settlements (BIS) estimates the size of the OTC equity-linked options market to be approximately US $5.7 trillion at the end of 2006 as measured by the total notional amount outstanding (Bank of International Settlements 2007), an increase of almost 58% from just 2 years earlier (see Exhibit 15.3), although a significant part of this increase can be attributable to growth in Asian equity option markets.

The primary users of exotic option instruments have been institutional investors such as banks, corporations, hedge funds, sovereign investment entities, and highly sophisticated individual investors as a way to generate additional alpha and to hedge risks. As a wider range of retail and institutional investors develop a better understanding of exotic options, the amount of equity-linked options traded is likely to rise.

Proportion of Total OTC Options Market by Asset Class

Interest Rate 70%

Exhibit 15.2 Proportion of total over-the-counter (OTC) options market by asset class

Proportion of Total OTC Options Market by Asset Class

Interest Rate 70%

Commodity

Commodity

Exhibit 15.3 Notional size of over-the-counter (OTC) contracts traded

Notional Size of OTC Equity Contracts Traded

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