FMP 4: Introduction to Derivatives

An exchange is a venue where investors trade contracts that the exchange itself has defined and standardized. Over-the-counter markets have no venue: participants contact each other directly, sometimes through a broker acting as intermediary, and settle the terms between themselves.

The Chicago Board of Trade (CBOT) opened in 1848 so that farmers and merchants had somewhere to deal with one another, and in 1973 it launched the Chicago Board Options Exchange (CBOE), which set out precise contract terms and listed call options first, with put options following in 1977. Trading once ran on the open-outcry system, with traders shouting and signalling by hand in a pit, while computers now match buyers with sellers. The flash crash of 2010, in which markets dropped about 7% inside 15 minutes and then recovered, came partly from the unintended consequences of a trading algorithm.

How the over-the-counter market is organized

Nothing over the counter obliges anyone to use a standard contract, and participants divide into end users and dealers. End users, a group covering corporations, fund managers and financial institutions of other kinds, want either to shed a risk or to acquire an exposure. Dealers are large financial institutions quoting bid and ask on commonly traded derivatives, and a dealer holding a position taken from an end user normally lays the risk off with another dealer, in the interdealer market.

Dealers trading with each other frequently work through an interdealer broker, and what the broker sells is discretion: the dealer avoids advertising what it needs to do, and the client’s name stays hidden until the trade is finalized. Once the market knows a dealer must unload a large exposure, other traders deal ahead of it.

Little of this was regulated before the credit crisis. Standardized derivatives traded between dealers in the United States must now, wherever possible, go through platforms known as swap execution facilities, where participants post bid and ask prices much as on an exchange. A central counterparty (CCP) must be used for standardized transactions between dealers, and every trade must be reported to a central registry.

Each channel buys something and gives something up. An exchange writes the contract for you, so the asset, the size and the maturity dates are fixed rather than negotiable, and that uniformity concentrates buyers and sellers into one instrument, which makes a position easy to unwind. Credit risk is very small because the exchange stands in the middle, and prices are posted publicly. What is lost is fit: a treasurer whose exposure is 1.3 million euros settling mid-month cannot buy exactly that.

The over-the-counter market reverses the trade-off. Two parties may agree any maturity, any size and, for an option, any strike price, which is why corporate hedgers go there. Against that, each side takes on the credit risk of the other, unwinding is harder because the contract is not interchangeable, and pricing is less visible than a public order book.

How the size of the two markets is measured

The Bank for International Settlements has collected figures since 1998, and the two series measure different things. For exchange-traded contracts the statistic is the value of the assets underlying the positions outstanding; for over-the-counter contracts it is the total principal underlying the transactions outstanding. Neither is the value of the transactions. Take an option over 100 shares, each of them worth USD 40 per share, carrying a right to buy at USD 45 per share: the statistics record it at USD 4,000, which is 100 multiplied by 40.

Source: Bank for International Settlements. The final column and last row are calculated from the reported figures.

Both markets grew by a factor of about 9, and the over-the-counter market stayed roughly five times the exchange-traded market. Against a world gross domestic product of about USD 85 trillion in 2018, the assets underlying outstanding contracts come to about nine times world output. The over-the-counter total fell between 2013 and 2015 through compression, in which participants restructure existing transactions so that the underlying principal is reduced.

Traded over the counter, a forward contract binds one party to buy an asset on a stated future date at a price fixed today, and binds the other to sell it on those terms. Its contrast is the spot contract, an agreement to buy or sell almost immediately. The buyer holds the long forward position and the seller holds the short forward position. The price written into the contract is the forward price, and once the contract is running that figure is the delivery price, written K.

Foreign currency is where these contracts are most heavily used. A company expecting to receive currency fixes its rate by selling that currency forward, while a company facing a payment buys it forward instead. A dealer posts a bid, at which it will buy, and an ask, at which it will sell, and forward rates are not the same as spot rates.

Both are straight lines crossing zero where the asset price equals the delivery price, which makes a forward contract a linear derivative. Neither party can walk away, so the loss on one side is exactly the gain on the other.

A futures contract provides much the same payoff as a forward contract and differs in where it lives. It trades on an exchange, which defines the asset, names the maturity dates available, and organizes trading so that credit risk, the risk that the agreement is not honored, stays very small.

The two instruments also cover different ground. Exchange rates and interest rates dominate the forward market, whereas futures span a far wider set of underlyings: agricultural products including wheat, corn and live cattle; metals including gold, copper, silver and platinum; equity indices such as the NASDAQ 100 and the S&P 500; energy products including natural gas, oil and electricity; real estate indices; temperature in particular cities; and bitcoin and other cryptocurrencies.

Source: the chapter’s descriptions of the three contract types.

An option hands its holder a right, and no obligation, to buy or to sell an asset at a price fixed in advance. Options trade on exchanges and over the counter, and every contract has two sides that are not symmetrical.

Under a call option the party with the long position may buy the asset from the party with the short position at an agreed figure, the strike price or exercise price, and the short position must then sell at that price. Under a put option the long position may sell the asset to the short position at the strike price. The date named in the contract is the expiration date. A European option may be exercised only at expiration, an American option at any point up to expiration.

The premium, and what option quotes look like

Entering a forward contract costs nothing, while buying an option costs a premium paid at the outset. The CBOE quoted call and put premiums on IBM options on December 23, 2019, with the stock itself bid at USD 135.66 against an ask of USD 135.68. Call premiums fall as the strike price rises, put premiums rise as the strike price rises, and premiums of both kinds rise with time to expiration. Bid-ask spreads on options run far wider, as a proportion of the price, than the spreads on the stocks themselves.

The four payoffs

Take a European call with strike price K and asset price S_T at expiration. The holder of the long position exercises when S_T is above K, paying K for something sellable at once for S_T, and lets the option lapse otherwise.

For a European put, the holder of the long position exercises when S_T is below K, selling for K an asset worth only S_T.

All four bend at the strike price, and two consequences follow. An option value responds non-linearly to the underlying, and it responds to the volatility of that underlying as well, since a wider spread of possible prices raises the chance of finishing on the profitable side of the kink.

Three motives bring traders to these markets. Hedgers arrive with an exposure and want less of it. Speculators arrive with a view and want exposure to it. Arbitrageurs want a profit independent of which way anything moves.

Hedgers

A hedger uses derivatives to reduce or eliminate an existing risk exposure. Forward contracts do this by fixing a rate; options give downside protection while leaving the upside in place. Picture a corporate treasurer facing a payment of 1 million euros in six months who buys a European call option on that amount, struck at USD 1.1150. Should the rate at maturity sit above the strike, the treasurer exercises and takes the euros at USD 1.1150; should it sit below, the option goes unused and the currency is bought more cheaply in the market.

Turn the exposure around. A treasurer expecting to receive 1 million euros six months out buys a European put option struck at the same USD 1.1150, exercises it whenever the rate ends below the strike, and so sells the currency for USD 1.115 million; a higher rate leaves the option unused and the euros are sold in the market. A forward contract locks in the price of a future transaction; an option protects against an adverse move and leaves favorable moves available.

That flexibility is not free. Locking a rate in through a forward costs nothing beyond the bid-ask spread, whereas the premium on either of those options over 1 million euros, struck at USD 1.1150, might come to USD 40,000. Raising the strike on a call, or lowering it on a put, cuts the premium and weakens the protection by the same movement.

Speculators

Derivatives let a trader take a large position with a small outlay, an effect much like leverage. Suppose a stock trades at USD 40, a trader expects it to rise over the next three months, and a call option struck at USD 42 costs USD 2. One route is to buy 100 shares for USD 4,000; the other is to spend that USD 4,000 on 2,000 options.

Source: the chapter’s comparison of the two strategies, ordered from the highest share price down, with the final column calculated as the difference.

Take the outcome at USD 45. Buying shares earns USD 5 on each of 100 shares, a profit of USD 500. The options allow 2,000 shares worth USD 45 to be bought for USD 42, generating USD 6,000, and after the USD 4,000 initial cost the profit is USD 2,000. So the option strategy is four times as profitable at USD 45 and twelve times as profitable at USD 50, while at or below USD 42 the whole USD 4,000 is gone. A futures position expresses the same view differently: its payoff runs one for one with the price in both directions, with no premium at stake and no floor under the loss.

Arbitrageurs

Arbitrage exploits prices that are inconsistent with one another across two or more markets, and it earns a profit without taking a view. The classic version sets a spot price against a forward price and a borrowing rate.

The variety of participants in derivatives markets is a strength and a large part of why these markets have grown. It also carries a hazard, because the leverage available to a speculator means very large risks can be taken with very little money.

Successful speculation is rewarded heavily, and a trader mandated to hedge or to seek arbitrage opportunities may find it more attractive than the job description. Someone who has lost money then tries to win it back with a larger position, and when the recovery fails to arrive the position grows again and again until the losses turn catastrophic.

Four episodes illustrate the sequence. John Rusnak at Allied Irish Bank lost USD 700 million trading foreign currencies and concealed it behind fictitious option trades. Nick Leeson at Barings Bank lost about USD 1 billion on unauthorized bets on the direction of the Nikkei index. Jerome Kerviel at Societe Generale lost about USD 7 billion on equity index speculation conducted under the appearance of arbitrage. Kweku Adoboli at UBS lost about USD 2.3 billion on unauthorized speculative positions in stock market indices.

Risks built into the instruments sit alongside that. An over-the-counter contract exposes each party to the possibility that the other fails to honor it, which is why standardized dealer trades now pass through a central counterparty. Options add sensitivity to volatility, so a position can lose money even when the underlying finishes where it was expected to. None of this argues against derivatives; it argues for controls that keep the traded book inside its mandate.