Introduction

• Derivatives are contracts whose values depend on (or derive from) the values of one or more financial variables (e.g., equity prices, exchange rates, and interest rates). Each of these variables is referred to as the underlying.
• Derivatives can be categorized into linear and non-linear products.
  • Linear derivatives provide a payoff that is linearly related to the value of the underlying asset(s). Forward contracts are an example of linear derivatives.
  • Non-linear derivatives provide a payoff that is a non-linear function of the value of their underlying assets. Options are examples of non-linear derivatives.
• The value of the underlying(s) is central to the valuation of both linear and non-linear derivatives. Other variables (e.g., interest rates and volatilities) can also play an important role.
• Derivatives now trade on exchanges as well as in over-the-counter markets. Both types of markets have experienced unprecedented growth as derivatives have become widely used.

• Derivatives are used in several ways (all points will become more clear as you progress)
  • Derivatives are used by companies to manage interest rate risk, foreign exchange risk, and the risk arising from commodity price changes, etc.
  • Derivatives are sometimes added to corporate bond issuances. They can give bond issuers the right to repay bonds early, or give bond holders the right to demand early repayment. Sometimes, bond holders have the right to convert a bond into equity of the issuing company.
  • Employee compensation plans sometimes give employees options to buy shares from the company at future times for a predetermined price.
  • Capital investment opportunities often have embedded options. For example, a company embarking on an investment may be able to abandon it if things go badly or expand if things go well. These are referred to as real options because they involve physical assets (rather than financial assets). It is now a common practice to consider real options when valuing capital investment opportunities.
  • Homeowners sometimes have derivatives embedded in their mortgages. If interest rates decline, for example, a homeowner can have the right to repay the mortgage early and refinance at a lower rate.

• The underlyings in derivatives are often financial variables (e.g., interest rates, exchange rates, and stock prices). However, almost every observable variable can be an underlying for a derivative. Examples include:
  • The price of hogs
  • The price of electricity in a particular region
  • The amount of snow falling at a certain ski resort
  • The temperature at a weather station
  • Earthquake damage claims made by an insurance company’s policyholders
  • The lifespan for a representative group of 1,000 people
• Derivatives can be used for either hedging or speculation. If a trader has an exposure in an asset class, a derivatives trade can reduce that exposure. If the trader has no exposure, however, that same trade is speculative. Speculation can be extremely risky.
• Derivatives have been criticized for their role in the 2007–2008 credit crisis. In the years leading up to the crisis, banks in the United States relaxed their lending standards on mortgages. This created a huge number of subprime mortgages (“subprime” means mortgages to less creditworthy borrowers). Furthermore, banks did not simply keep these mortgages on their balance sheets. Instead, they bundled them into portfolios and created complex derivatives whose values depended on the losses from defaults on these mortgages. The increased availability of mortgages led to a significant increase in demand for housing that in turn led to a sharp increase in house prices. Meanwhile, defaults and foreclosures began to rise as many subprime borrowers realized they could not afford their mortgages.
• This was made worse by a rise in mortgage interest rates. There was an increase in the supply of houses for sale and a reduction in housing prices. This in turn led to negative equity positions (i.e., situations where the amount owed on a mortgage was greater than the value of the house).
• Some homeowners with negative equity defaulted even though they could afford to service their mortgages, depressing house prices even further. As a result, there were losses on many of the derivatives created from mortgages, and investors throughout the world (temporarily) lost their appetite for risky debt of any sort. As a result, the world was plunged into the worst recession in 75 years.
• Derivatives also have many attractive features. They allow risks to be transferred from one party to another in ways that benefit both sides. The following are examples:
  • Corporate treasurers can manage exchange rate risk, interest rate risk, and commodity price risk in ways that would otherwise not be possible.
  • Fund managers can diversify their exposures using derivatives.
  • Ski slope operators can avoid being forced out of business due to a single unseasonably warm winter.
• The challenge for regulators is to find ways to benefit from derivatives while discouraging extreme speculative behavior (i.e., where huge risks are taken or unnecessarily complex instruments are created).
• Derivatives trade on exchanges as well as in over-the-counter markets. An exchange is a market where investors trade standardized contracts that have been defined by the exchange. Over-the-counter markets are markets where participants contact each other directly (or possibly by using a broker as an intermediary) to trade. The operation of the two markets will be discussed in detail in later chapters.

Exchange-Traded Markets

• Derivatives exchanges have existed for many years. For example, the Chicago Board of Trade (CBOT) was established in 1848 to allow farmers to trade with merchants. Within a few years, a forerunner of futures contracts known as “to-arrive” contracts began to be traded. There are now futures exchanges in many parts of the world.
• In 1973, the CBOT launched the Chicago Board Options Exchange (CBOE). The CBOE established well-defined contracts and a mechanism to minimize the probability of losses from defaults. Today, the CBOE is one of many exchanges around the world trading options on stocks and stock indices.
• Traditionally, derivatives exchanges have used what is referred to as the open-outcry system. This involves traders meeting on the floor of the exchange and indicating their proposed trades with hand signals and shouting. (Tall traders may have had an advantage because it was easier for them to attract the attention of other traders.) Most trading is now done electronically, however, with computers being used to match buyers and sellers. Sometimes electronic trading is initiated by computer algorithms without any human intervention at all.

Over-The-Counter Markets

• An advantage of over-the-counter (OTC) markets is that the contracts traded do not have to be the standard contracts defined by exchanges, and market participants can trade any contracts they like.
• OTC market participants can be categorized as follows:
  • End users are corporations, fund managers, and other financial institutions who use derivatives to manage their risks or to acquire specific exposures.
  • Dealers are large financial institutions that provide both bid and ask quotes for commonly traded derivatives. They are also prepared to make one-sided quotes for highly structured derivatives when requested. Dealers typically offset the risks from their trades with end users by trading with other dealers in what is referred to as the interdealer market.

• While end users typically contact dealers directly, dealers often use interdealer brokers when trading with other dealers. The advantage of an interdealer broker is that a dealer does not have to indicate their desired trades to other dealers. When finding a dealer to be a counterparty to its client, the broker does not reveal its client’s name until the trade has been finalized.

• Before the 2007–2008 credit crisis, the over-the-counter market was largely unregulated. Since the crisis, there have been several new regulations. The following are examples:
  • In the United States, standardized OTC derivatives traded between dealers must (whenever possible) be traded on platforms known as swap execution facilities. These are like exchanges and feature market participants posting bid and ask prices.
  • A central counterparty (CCP) must be used for standardized transactions between dealers. (CCPs are discussed in the next two chapters.)
  • All trades must be reported to a central registry. (Previously, trades in the OTC market were considered private transactions, and there were no reporting requirements.)

Market Size

• The Bank for International Settlements began collecting data on derivatives markets in 1998. Statistics for the exchange-traded market show the value of the assets underlying outstanding exchange-traded contracts, while statistics for the OTC market show the total principal underlying outstanding transactions.

	Exchange-Traded Market	Over-The-Counter (OTC) Market
June 1998	13.3	72.1
June 2017	81.0	531.9

Value of underlying assets in derivatives markets in June 1998 and June 2017 (trillions of USD)

• This figure illustrates how the sizes of the two markets have changed between 1998 and 2017.

• It is important to emphasize that the size statistics do not provide the value of the transactions.
  • In the case of the exchange-traded market, they measure the value of the underlying assets. If an option gives the holder the right to purchase 100 shares worth USD 40 per share for USD 45 per share, for example, the size of the contract would be recorded as USD 4,000(=100×40).
  • In the case of the OTC market, the statistics measure the principal underlying outstanding transactions. This means that a forward contract to buy one million British pounds at an exchange rate of USD 1.2500 in the future would be recorded at the current value of one million British pounds and not at the value of the forward contract (which might be only a few thousand dollars).
• The decline in the size of the OTC market between 2014 and 2017 can be attributed to the widespread use of compression. This is a procedure where two or more market participants restructure transactions with the result being that their underlying principal (and therefore the amount of capital they are required to keep) is reduced. Compression will be explained later.

Forward Contracts

• A forward contract is an over-the-counter contract where one party agrees to buy an asset for a predetermined price at a future time and the other party agrees to sell the asset for the predetermined price at the future time. Forward contracts can be contrasted with spot contracts, which are agreements to buy or sell an asset almost immediately.
• The party that has agreed to buy has a long forward position while the party that has agreed to sell has a short forward position. The specified asset price in a forward contract is referred to as the forward price. The determination of forward prices will be discussed later.

Forward Contracts Example

• Forward contracts on foreign currency are very popular. If Company A knows it will receive a certain amount of a foreign currency at a certain future time, it can use a forward contract to lock in the exchange rate by selling the foreign currency at the forward exchange rate. Similarly, if Company B knows that it will pay a certain amount of a foreign currency at a certain future time, it can enter into a long forward contract to buy the foreign currency at the forward exchange rate.
• This table shows quotes for spot and forward contracts on the USD–euro exchange rate (as they might have been made by a derivatives dealer) on June 8, 2018. The bid price is the price at which the dealer is prepared to buy and the ask price is the price at which the dealer is prepared to sell.

	Bid	Ask
Spot	1.1768	1.1771
One-Month Forward	1.1802	1.1805
Three-Month Forward	1.1858	1.1862
Six-Month Forward	1.1944	1.1948

• Forward contracts are linear derivatives because their payoff is linearly related to the value of the underlying asset at maturity.

Forward Contracts – Long Position

• In general, if   is the asset price at the maturity of a forward contract and K is the delivery price (i.e., the forward price when the contract was initiated). The payoff from a long forward contract on one unit of the asset is

Forward Contracts – Short Position

• In general, if is the asset price at the maturity of a forward contract and K is the delivery price (i.e., the forward price when the contract was initiated). The payoff from a short forward contract on one unit of the asset is:

Futures Contracts

• Forward contracts are traded in the over-the-counter market. A futures contract provides a similar payoff to a forward contract, but it trades on an exchange. The exchange defines the asset and specifies the maturity dates that can be traded. The exchange organizes trading so that there is very little credit risk (i.e ., risk that the agreement will not be honored) even though the two parties to a trade may not know each other.
• While forward contracts trade most actively on a small number of underlying assets (e.g., exchange rates and interest rates), futures trade on a wide range of other underlyings. This includes:
  • The prices of agricultural products such as corn, wheat, and live cattle;
  • The prices of metals such as gold, silver, copper, and platinum;
  • Equity indices such as the S&P 500 and the Nasdaq 100;
  • The prices of energy products such as oil, natural gas, and electricity;
  • Real estate indices;
  • Temperatures in particular cities; and
  • Cryptocurrencies like bitcoin.

Options

• Options are derivatives that give the holder the right (but not the obligation) to buy or sell an asset at a predetermined price in the future. They trade on exchanges as well as in the over-the-counter market.
• In the case of a call option, the party with a long position has the right (but not the obligation) to buy an asset from the party with a short position for a certain price (known as the strike price or exercise price) at one or more future times. If the party exercises this right, the party with the short position must sell the asset for the strike price.
• A put option is a contract where the party with a long position has the right (but not the obligation) to sell an asset to the party with a short position for a certain price (the strike price) in the future. If the party exercises this right, the party with the short position must buy the asset for the strike price.
• The date specified in an options contract is known as the expiration date (or maturity date). A European option can only be exercised at expiration. An American option can be exercised at any time up until expiration.
• There was no cost involved to enter into a forward contract, but entering into an option contract requires a price (known as the premium) to be paid at the outset. The options on stocks traded by exchanges are American. Options trade with several different future expiration dates.

Strike Price (K)	September 21, 2018		December 21, 2018		June 21, 2019
$	Bid	Ask	Bid	Ask	Bid	Ask
140	9.70	9.80	11.45	11.65	14.20	14.45
145	6.35	6.45	8.40	8.55	11.45	11.65
150	3.80	3.90	5.90	6.05	9.05	9.25
155	2.14	2.18	4.00	4.10	7.00	7.25

Call option premiums on IBM on June 11, 2018, with different expiration dates

Strike Price (K)	September 21, 2018		December 21, 2018		June 21, 2019
$	Bid	Ask	Bid	Ask	Bid	Ask
140	2.76	2.81	5.00	5.15	8.65	8.90
145	4.50	4.65	7.05	7.15	10.85	11.10
150	7.10	7.25	9.65	9.80	13.45	13.70
155	10.55	10.65	12.75	12.95	16.40	16.70

Put option premiums on IBM on June 11, 2018, with different expiration dates

• Call option prices decrease as the strike price increases, whereas put option prices increase as the strike price increases. An option price increases as the time to maturity increases.
• Bid-ask spreads (particularly if they are expressed as a proportion of the price) are much higher for options on stocks than they are for the stocks themselves.

Call Options – Long Position

• Consider a European call option that can be exercised at time T. Suppose that K is the strike price and S_T is the option price at time T. In this case, the trader who has bought the option has the right to buy the asset for K

• Long Position –
  • If S_T > K, the trader exercises the option. This means that he or she pays K for an asset that can be immediately sold for . The payoff to the trader is therefore S_T – K
  • If  S_T < K, the option is not exercised and the payoff to the trader is zero.

Putting the above two outcomes together, the option payoff is

max(S_T – K, 0)

Call Options – Short Position

• Consider a European call option that can be exercised at time T. Suppose that K is the strike price and is the option price at time T.

• Short Position –
  • If S_T > K, this trader must sell an asset worth for K.

• • If S_T < K, the trader is not required to make the sale.

So, the payoff of the short position is simply the negative of the payoff of the long position, which is

max⁡(S_T – K, 0)

Put Options – Long Position

• Consider a European put option that can be exercised at time T. Suppose that K is the strike price and is the option price at time T. In this case , the trader who has bought the option has the right to sell the asset for K.

• Long Position –
  • If < K, the trader will exercise the right to sell the option, and an asset worth S_T is then sold for K. The payoff to the trader is therefore K – S_T
  • If > K, the option is not exercised, and there is no payoff to the option owner.

Putting the above two outcomes together, the option payoff is

max(K – S_T, 0)

Put Options – Short Position

• Consider a European put option that can be exercised at time T. Suppose that K is the strike price and S_T is the option price at time T. In this case, the trader who has bought the option has the right to sell the asset for K

• Short Position –
  • If < K, the trader (who is short the put option) must buy an asset worth S_T for K. The payoff to the trader is therefore .

• • If > K, and the trader is not required to buy the asset.

So, the payoff of the short position is simply the negative of the payoff of the long position, which is

-max(S_T – K, 0)

Options – Non Linear Characteristic

• Options are more complex derivatives than forward or futures contracts. Their payoffs are non-linear functions of the underlying asset price. This has two consequences.
  1. The value of an option is a non-linear function of the value of the underlying.
  2. The value of an option is dependent on the volatility of the underlying.

Market Participants

• There are three main categories of traders in derivatives markets.
  • Hedgers
  • Speculators
  • Arbitrageurs

Hedgers

• Hedgers use derivatives to reduce or eliminate risk exposure.
• Forward contracts as well as options can also be used to hedge currency risk. It does not cost anything (except for the bid-ask spread) to lock in the forward price. By contrast, an option requires that the buyer pay a premium. Unlike forward contracts, options allow traders to get downside risk protection while preserving some upside potential. While a forward contract locks in the price applicable to a future transaction, an option provides protection against adverse price movements.

Speculators

• Derivatives also allow risks to be taken with a relatively small upfront payment. In this sense, they have much the same effect as leverage and can be attractive to speculators.

Asset Price in 3 Months (USD)	Profit from Asset Purchase (USD)	Profit from Options (USD)
30	$3000	-$12000
35	-$1500	-$12000
40	0	-$12000
45	$1500	$8000
50	$3000	$28000

Profits from two alternative strategies that are speculating that the price of an asset will increase

Arbitrageurs

• Arbitrage involves taking advantage of inconsistent pricing across two or more markets.

Derivatives Risks

• The leverage that speculators can obtain means that it is very easy for traders to take significant risks. A key problem is that the rewards from successful speculation are very high and many traders are tempted to speculate even when their mandate is to hedge risks or to search for arbitrage opportunities. If controls are not in place, these traders may start speculating without the knowledge of others in their organization. A speculating trader who loses money may seek to offset losses by taking increasingly large and risky positions. If the offsetting gains do not materialize, the trader may increase the risks taken again and again until the losses reach catastrophic levels. Examples of such traders include:
  • John Rusnak at Allied Irish Bank, who lost USD 700 million trading in foreign currencies and managed to conceal his losses by creating fictitious option trades;
  • Nick Leeson at Barings Bank, who lost about USD 1 billion by making unauthorized large bets on the future direction of the Nikkei index and managed to hide his losses from his superiors for some time;
  • Jérôme Kerviel at Société Générale, who lost about USD 7 billion by speculating on equity indices while giving the appearance of being an arbitrageur;
  • Kweku Adoboli at UBS, who lost about USD 2.3 billion taking unauthorized speculative positions in stock market indices.