Derivative Securities

I DEFINITIONS AND OTHER BASIC CONCEPTS

A WHAT ARE DERIVATIVE SECURITIES?

It is difficult to speak generally about derivative securities. It is possible to observe that a derivative security involves a contingent claim; it is a security that has some essential feature, typically the price, that is derived from some future event. This event is often, though not always, associated with a security or commodity delivery to take place at a future date. The contingent claim can be combined with other security features or traded in isolation. This definition is not too helpful because financial markets are riddled with contingent claims. Sometimes the contingent claim is left bundled with the spot commodity, in which case the derivative security is also the spot commodity (e.g., mortgage-backed securities). Yet, the term “derivative security” is usually restricted further to only include cases where the contingent claim is unbundled and traded as a separate security, effectively forwards, futures, options, and swaps. In what follows, this class of unbundled contingent claims will be referred to as derivatives securities.

Derivative securities trading is definitely not a modern development. The implicit and explicit embedding of derivative features was common in the types of securities traded in early markets. Early examples of securities with derivative features include claims on the 14th century Florentine mons that had a provision for redemption at 28% of par, though that provision was seldom exercised; 16th-century bills of exchange that combined a loan with a forward foreign exchange contract; and 18th century life annuities that featured terms to maturity dependent on specific life contingency provisions (Poitras, 2000). The “to arrive” contracts traded on the Antwerp bourse during the 16th century may be the first instance where a contingent claim was unbundled and traded as a separate security on an exchange. Previous to this time, such derivative security transactions had been limited to private deals between two signatories executed using escripen or notaries.

In addition to securities with embedded derivative features, early financial markets can be credited with beginning exchange trading in modern derivative security contracts.1 Though the precise beginnings of option trading are difficult to trace, it is likely that there was trading in options, as well as “to arrive” contracts, on the Antwerp bourse during the early 16th century (Poitras, 2000). By the mid-17th century, trade in options and forward contracts was definitely an integral activity on the Amsterdam bourse (de la Vega, 1688). Trading in both options and forward contracts was an essential activity in London’s Exchange Alley by the late 17th century (e.g., Houghton, 1694). The emergence of exchange trading of futures contracts can be traced to either 19th century Chicago (Hieronymous, 1977) or 18th century Japan (Schaede, 1989).

From these early beginnings, modern markets have achieved full securitization of a wide range of derivative securities. The modern Renaissance in derivative security trading has posed considerable problems for the accounting profession (e.g., Gastineau, 1995; Perry, 1997). In order to address the accounting problems raised by the use of derivative securities by firms for risk management and other purposes, the notion of “free standing derivatives” was introduced. This reference to free standing derivatives is precise accounting terminology borrowed from the financial accounting standard FAS 133 (FASB, 1998). Being “free standing”, derivative securities pose fundamental problems for conventional methods of preparing accounts. This point has not been lost on the accounting profession, which has been engaged in ongoing attempts to produce a set of standards that permit an accurate financial presentation of the accounts of the firm and do not permit substantial discretionary variation in the accounts. In a perfect world, two otherwise identical firms, both involved with using derivative securities, would not be able to present accounts that were substantively different, based on discretionary accounting choices, such as the method used to recognize gains or losses on the offsetting spot position.

The accounting profession is acutely aware of the question: What are derivative securities? The main difficulty for accountants is that the derivatives are free standing.2 When the contingent claim is unbundled from the underlying transaction, it is difficult to attach that security back to the transaction that motivated the derivative security position. For obvious reasons, derivative securities require mark-to-market accounting. Yet, accounting for cash positions can be flexible: book value or market value, depending on the situation. Because of the potential for substantial discretionary manipulation of the accounts, accounting standards such as FAS 133 and 138 have been introduced. Under recent standards, the narrow class of unbundled contingent claims is now classified as free standing derivatives. As such, more flexible rules have been introduced to ensure that there is accurate hedge accounting for firms using these securities. This category excludes fixed income securities with embedded derivative features, such as mortgage-backed securities and callable or convertible bonds.3 A key implication of all this for non-accounting professionals is that, due to the introduction of FAS 133, substantially enhanced information about derivatives positions is now available in annual reports and other sources of financial information for publicly traded companies (e.g., 10-Ks).

This approach to defining derivative securities is not without conceptual difficulties. An essential feature of the free standing derivative securities is the action of setting a price today for a transaction to take place at a date in the future. However, this feature is also present in other types of financial securities. A bond, for example, sets a price today for a sequence of fixed cash flows that will be received in the future. Even a common stock sets a price today for a sequence of uncertain cash flows that will be received in the future. One element that distinguishes free standing derivative securities from financial securities such as bonds is the timing of the settlement. A forward contract involves settlement and delivery at maturity, while a bond involves settlement today with delivery in the form of payments at future maturity dates. Using this approach, an option contract is somewhat anomalous, requiring a payment today to acquire the right to make a settlement at a price that is set today. The distinction between the various cases actually lies with the respective cash flows.

B SOME DEFINITIONS

At this point, some of the jargon that characterizes derivatives trading will be introduced. For practical purposes, an attempt has been made to use the terminology of the marketplace. The occasionally colorful language is often transparent in intent but confusing in application. For example, in futures and forward markets it is conventional to use the following:

However, in options markets a long position refers to the purchase of a call or put option, while a short position refers to the writing of a call or put option. This terminology applies even though purchasing a put option involves paying a premium for the right to sell for future delivery. In turn, a short position in the spot commodity market involves borrowing the commodity under a short sale agreement which is then sold in the spot market, generating a cash inflow. A long position in the spot commodity would involve a current cash outflow in exchange for possession of the physical commodity.

The use of analytical concepts such as profit functions requires introducing some notation that will be used throughout the book:

For consistency, it has to be that T ≥ N ≥ t. In much of what follows, the assumption, F(T,T) = S(T) is made in order for the price of a futures contract observed on the delivery date t = T to be equal to the price of the deliverable commodity. In effect, the spot commodity is taken to be the deliverable commodity. This condition is readily satisfied for forward contracts but requires assuming away the possibility of cross hedging if futures contracts are involved. Conventional time dates that will be used are t = 0 and t = 1 with N for contracts that are nearby or closer to delivery and T for contracts that are deferred or farther from delivery.

Using a strictly legal definition, it is possible to be reasonably precise about what constitutes a futures contract. However,...