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905N13
INTRODUCTION TO DERIVATIVES
Jaclyn Grimshaw wrote this note under the supervision of Professors Walid Busaba and Zeigham Khokher solely to provide material
for class discussion. The authors do not intend to illustrate either effective or ineffective handling of a managerial situation. The
authors may have disguised certain names and other identifying information to protect confidentiality.
Ivey Management Services prohibits any form of reproduction, storage or transmittal without its written permission. Reproduction of
this material is not covered under authorization by any reproduction rights organization. To order copies or request permission to
reproduce materials, contact Ivey Publishing, Ivey Management Services, c/o Richard Ivey School of Business, The University of
Western Ontario, London, Ontario, Canada, N6A 3K7; phone (519) 661-3208; fax (519) 661-3882; e-mail cases@ivey.uwo.ca.
Copyright © 2008, Ivey Management Services
Version: (A) 2009-10-04
A derivative is a financial instrument whose value, as its name suggests, is derived from the attributes of
the underlying asset or security on which it is based. Many different derivative securities are available in
the world markets, including forwards, futures, options, rights, warrants and swaps. This note introduces
the basics concepts, terminology and strategies associated with forwards, futures and options.1 The other
derivative securities (rights, warrants and swaps) will be discussed briefly in Exhibit 1.
The trading of a derivative security involves the trading of the right or obligation to take further strategic
action with respect to the underlying asset or security. Note, however, that the derivative itself trades
independently of the asset or security on which it is based. This trading can take place either on a
formalized derivatives exchange or as an over-the-counter (OTC) trade, directly between two parties.
Some of the most common uses for derivative securities include capital budgeting, insurance, hedging a
position,2 providing employee and executive compensation, capital raising, and investor speculation and
arbitrage.3 Given their complex nature and the riskiness of derivative securities when compared with other
securities, such as stocks and bonds, these securities have traditionally been the domain of institutional
investors and hedge funds. Although derivatives’ trading is still largely dominated by institutions and
funds, because of increased standardization and improved access to trading platforms, derivatives have
begun to attract increasing interest from retail investors.4
1
This note focuses on simple or “plain vanilla” options. All references to options refer to vanilla options.
Hedging refers to the practice of eliminating a “natural exposure” by taking on a security whose payoff is negatively
correlated to the original position. The net effect is to protect the investor from price fluctuations.
3
Arbitrage entails the simultaneous purchase of two separate but related securities with the intention of profiting from price
discrepancies. Thus, arbitrageurs attempt to profit from market inefficiencies.
4
An institutional investor is an organization that invests its own assets and assets held in trust for others, such as a pension
fund or mutual fund. Retail investors, also known as private investors, are individuals who buy and sell securities on their
own behalf.
2
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FORWARDS AND FUTURES
Forward contracts facilitate the trading of commodities between two parties. Commodity assets on which
forwards trade today include agricultural products, livestock, metals and energy products, such as oil and
gas. In addition to these commodities-based forwards, forward contracts also trade on a variety of
underlying financial assets, including foreign currencies and market indices. In fact, a forward contract can
be written and traded on virtually any asset for which a market exists.
A forward contract is a legally binding agreement between two parties to deliver, or take delivery of, an
asset at a future maturity date for an agreed upon forward price. The forward price is set at inception of the
contract. When the contract matures, the underlying asset must be purchased, or delivered (depending on
the position taken in the contract), for the forward price irrespective of the prevailing market (or spot)
price. By locking in the price to be paid at maturity, the holder (or buyer) of the contract is protected from
an increase in the spot price of the underlying asset and, conversely, the seller is protected from a decrease
in the spot price. In exchange for this downside protection, both parties forgo any upside that would have
resulted if the spot price were to have moved in a favorable direction for either of them.
The holder of a forward contract has taken a long position. A long investor in any asset may be bullish,
believing that the asset’s market value will appreciate and thus result in a profit. A long forward position
also benefits from an increase in the underlying asset’s spot price. There must be counterparty to the holder
of a forward contract; this party is known as the seller (or writer). The seller of the forward contract
guarantees the price at which the underlying asset will be sold and delivered. The seller’s position is
referred to as a short forward. An investor with a short position in an asset may be bearish, believing that
the price of the held asset will decline and profits if it does. A short forward position also profits when the
asset value falls. Neither the buyer nor the seller incurs any expense when entering into a forward contract,
though both are legally bound by its terms and obligations. Parties to a forward contract, however, are
usually allowed to transfer their obligations to another willing party.
A futures contract is similar to a forward in that it is also a binding contract to deliver or take delivery of a
commodity or financial asset based on the terms of the contract, with two key distinctions:
1. Futures have standardized terms and are traded on organized securities exchanges. A clearinghouse
serves as the technical counterparty to the contract. Forwards, on the other hand, are traded over-thecounter, directly between two parties, and in the case of physical delivery or settlement, the forward
contract specifies the exact party to whom the delivery and payment must be made.
2. Futures contracts are settled daily by marking-to-market the asset’s value and making adjustments to a
related margin account.5 In contrast, forwards typically settle at maturity or in accordance with an
agreed-upon schedule if the transaction is collateralized.
These two distinctions make futures less risky and thus more prevalent than forwards in today’s markets.
Futures are liquid and are backed by more than just the creditworthiness of the individual parties to the
contract. In fact, exchange-traded derivatives all have the same effective default and settlement risk,
limited to the default risk of the clearinghouse itself. It should be also be mentioned that a majority of
future and forward contracts are cash-settled as opposed to an individual party taking physical delivery of
the commodity or financial asset.
5
A margin account is a brokerage account with a specified minimum balance, or margin, that an investor holds with a broker
as a form of security against borrowed assets.
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A large number of futures and options exchanges operate worldwide, ranging in size and product scope,
and many are security-specific or region-specific.
The IntercontinentalExchange, or ICE, operates as a global commodity and financial derivatives platform
for the futures, options and OTC markets. Through its operating subsidiary, ICE Futures Europe, ICE is the
largest electronic energy futures exchange and the company further conducts soft commodity futures and
options markets through its U.S. regulated subsidiary, ICE Futures U.S.
As part of the NYSE Euronext, the first truly global stock exchange that operates multiple securities
exchanges, the London International Financial Futures and Options Exchange (LIFFE or Euronext.liffe)
offers a range of futures and option products to prospective investors. The CME Group, which formed as
the result of the merger between the Chicago Mercantile Exchange (CME) and the Chicago Board of Trade
(CBOT) in 2007, is the world’s largest futures exchange handling more than one billion contracts per year.
On these exchanges, the active derivatives contracts are settled (or marked-to-market) daily, and the
counterparties of the contract settle profits and losses with the exchange’s clearinghouse through their
margin accounts.
OPTIONS: PUTS AND CALLS
Like other derivatives, an option is a contractual agreement between two counterparties based on an
underlying asset or security. In exchange for a fee, an option contract gives the holder the right, but not the
obligation, to engage in a future transaction (i.e. to buy or sell) the underlying asset at an agreed upon price
for either a specified period of time or at a specific point in time. The underlying asset or security in an
option contract can be common stock, bonds, an index, a futures contract or other such assets.
All exchange-traded options include the following contractual terms:
•
•
•
•
•
•
•
Type of Option: whether the option holder has the right to buy (a call option) or sell (a put option)
Style: determines the dates on or over which the option can be exercised
Underlying Asset: the security or asset on which the holder has contractual rights
Exercise (or Strike) Price: the price per unit of the underlying asset at which the holder can exercise
the contract (i.e. buy or sell the asset or security)
Expiry (or Expiration) Date: the last date the option can be exercised
Lot: the size of the option contract, usually consisting of lot sizes of 100 units of the underlying asset
or security
Settlement Terms: the methods of exchange and transaction
A call option provides the buyer (holder) with the right to purchase the underlying security at the exercise
price up to the expiry date. The seller (writer) of a call option is obligated to sell the underlying security at
the exercise price until the expiry date, if called to do so by the buyer. A put option provides the buyer
with the right to sell the underlying security at the exercise price up to the expiry date. The writer of a put
option is obligated to purchase the underlying security at the exercise price until the expiry date, if called
to do so by the buyer.
Option contracts are most commonly one of two styles: either American or European. American options
allow buyers to exercise their right on any trading day from the time of initial purchase up to the expiry
date. European options, on the other hand, may only be exercised on the expiry date itself. Both types of
options can be obtained either through an option exchange or privately as an over-the-counter trade.
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Exchange-traded options (also referred to as listed options) are similar to futures contracts in that they have
standardized contract terms and settle daily through a clearinghouse. Examples of exchange-traded options
include stock options, commodity options, bond options and index equity options. Over-the-counter
options are traded between two private parties and are not listed on an exchange. Similar to forward
contracts, the terms of an OTC option contract can be negotiated between the two counterparties and thus
also tend to be illiquid. Examples of OTC options include interest rate options and options on other
derivates, such as swaps.
The lifespan of an option ends on a specified expiration date. In North America, exchange-traded equity
options quote their expiration date as a month, and some may be traded or exercised on or up to the third
Friday of that month. In this case, the option contract ceases to exist on the following day (Saturday).
As an example, if the exercise price of an option is $50, and the contract holder exercises the option to
purchase the underlying security, then the buyer has employed the right to purchase 100 units or shares at
$50 each, regardless of the prevailing market price. This transaction requires a total cash outlay of $5,000
in exchange for the 100 shares of the underlying security, which are delivered from the counterparty in the
contract, with the settlement and delivery being coordinated by the clearinghouse as the intermediary.
Unlike forwards and futures, which are both zero-cost instruments, the buyer of an option pays a fee or a
premium to purchase the option. The premium is the value of the contract and is quoted in dollars per unit
of underlying security. In exchange for the premium, the buyer has purchased the right to use (or exercise)
the option. The option seller collects and retains the premium regardless of whether the buyer chooses to
exercise the option contract. Note that the buyer holds the absolute discretion on when (in the case of
American options) or whether to exercise the option to purchase; the seller must merely respond to the
buyer’s decision.
In summary, an option contract is purchased for a premium, which gives the buyer the contractual right to
take further action with regards to an underlying security or asset at a set exercise price for a period ending
on a specified expiry date. Table 1 below shows a sample option listing on Canadian National Railways
(CNR) common stock. The expiry date and exercise price are stated on the far left and pricing/premium
data is found in the middle of the table. The call options presented below expire in January and are
available for strike prices ranging from $66 to $70. The options quote includes information on the daily
volume traded, in lots of 100, and the open interest (the number of outstanding contracts in the given
series).
Table 1 - Excerpt from Montreal Exchange Online Option Quote for CNR
Series/Strike prices
Bid
Size
Bid
Price
Ask
Price
Ask Last
Net
Size Price Change High
05 Jan 66.000
05 Jan 68.000
05 Jan 70.000
(CNR AG)
(CNR AU)
(CNR AN)
25
25
25
3.10
1.55
0.55
3.25
1.70
0.65
Call
20
45
20
3.70
0.60
05 Mar 64.000
05 Mar 66.000
05 Mar 68.000
05 Mar 70.000
(CNR OH)
(CNR OG)
(CNR OU)
(CNR ON)
20
20
20
45
0.65
1.15
1.85
2.80
0.80
1.25
1.95
2.95
Put
55
15
15
35
0.60
1.15
2.05
(1.60) 3.70
(1.20) 0.60
0.10
0.35
0.10
0.60
1.15
2.05
Open
Interest
Low
Vol
3.70
0.60
10
10
20
20
6
0.60
1.15
2.05
11
10
40
209
120
42
46
Source: Montreal Exchange - Market Data and Quote, 07-Jan-2005
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A call option is referred to as in-the-money when the market price is greater than the exercise price of the
underlying security. When the market price for a put option is less than the exercise price it is in-themoney. Exercising an option that is in-the-money has a positive payoff for the buyer. When the exercise
price of either a call or put equals the market price, the option is referred to as at-the-money. In this
situation, a zero gain results for the holder and exercising the option is effectively the same as buying or
selling the underlying security on the open market (abstracting from the premium exchanged at inception).
A call option is out-of-the-money when its exercise price is greater than the market price and a put option is
out-of-the-money when its strike is below the market price. Exercising an option that is out-of-the-money
yields a net loss to the holder.
There are four distinct investment positions that can be taken with option contracts: call buyer, call seller,
put buyer and put seller.
CALL BUYER
The call buyer has purchased the right to buy the underlying asset or security in the future at a specified
exercise price. Option premiums are typically lower than the price of the underlying asset, allowing the
investor to purchase a larger number of options than units of the underlying asset and to potentially realize
a larger gain than if the asset had been purchased directly. Thus, options can act as a form of leverage for
an investor. Options can also be used to temporarily defer the purchase of the underlying asset, allowing
the investor to invest in a short-term security in the interim to gain additional income.
The call buyer is long on the underlying asset. The potential payoff available to a call buyer is illustrated in
Figure 1. The upside available to a call buyer is theoretically without limit and equals the security price at
maturity less the exercise price. At any point where the security or asset price is greater than the exercise
price, the payoff increases dollar for dollar with the asset’s or security’s value.
Figure 1 — Call Holder Payoff Diagram
Payoff
Security Price
Exercise Price
Note: The payoff diagrams in this note do not include the premium paid to purchase the option. To find the net profit or loss
to the investor, the premium paid for the option must be subtracted from the payoff for option holders and added to
the payoff for the option seller.
CALL SELLER
For the call seller, one motivation for writing the option is to earn the premium income. Regardless of
whether the option is exercised by the call buyer, the seller keeps the premium as compensation for taking
on the obligation to deliver the underlying security if called upon to do so.
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Writing the call option alone without owning the underlying security or asset is referred to as a naked
position. The payoff to the naked writer is zero, and the net profit is limited to the income received from
the premium paid. The loss for naked call writers, however, is theoretically unlimited as they are
contractually obligated to provide the underlying security at the specified exercise price; and in order to
cover, or close out, the position, they may be forced to purchase the asset or security at a higher price on
the open market. At any point where the security’s price is greater than the exercise price the call writer is
likely to be called to deliver the underlying security to the call buyer, and the loss increases dollar for
dollar with the increase in the security’s price (see Figure 2).
Figure 2 — Naked Call Seller Payoff Diagram
Payoff
Exercise Price
Security Price
A less risky position for the call writer to assume is to also own the underlying asset or security on which
the call is written. Holding the underlying asset and writing the call concurrently is referred to as a covered
position. The covered writer has effectively hedged the position in the call by owning the underlying asset.
The call seller has eliminated the risk of incurring a theoretically unlimited loss on the call in return for
giving up the capital gains on the underlying security itself.
Figure 3 — Covered Call Seller Payoff Diagram
Security Payoff
Combined Position – Covered Call
Payoff
Security Price
Exercise
Price
Naked Call Payoff
PUT BUYER
The put buyer has purchased the right to sell an asset or security in the future for the specified exercise
price. The put buyer need not own the underlying asset or security to enter into an option contract to sell
such asset or security, taking on a naked position. The naked put buyer achieves positive payoff if the asset
or security’s price decreases below the exercise price and it is purchased on the open market by the
investor to close out the position (see Figure 4). If the underlying asset or security’s price rises above the
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exercise price, the put option will go unexercised by the buyer and the naked put buyer incurs a net loss
equal to the premium paid.
Figure 4 — Naked Put Buyer Payoff Diagram
Payoff
Exercise Price
Security Price
When investors own the underlying asset or security on which they are purchasing the put (i.e., a covered
position), the option can be thought of as a form of insurance. That is, the investor pays a premium to be
protected in the event of a price decrease. In this case, the maximum loss associated with holding a put is
limited to the value of the premium paid to enter into the contract. The covered put buyer in fact has an
effective net gain when the asset or security’s prices rises equal to the appreciated price less the put
premium (see Figure 5).
Figure 5 — Covered Put Buyer Payoff Diagram
Security Payoff
Payoff
Combined Position – Covered Put
Naked Put Payoff
Security Price
Exercise Price
PUT SELLER
Similar to the call seller, the put seller may participate in option contract writing simply as a means to earn
additional income. A put seller receives the option premium as a tradeoff for taking on the obligation to
buy the security if called on to do so. Alternatively, the put seller may want to purchase the security but is
either unwilling or unable to purchase the security at the current market price. By writing a put, investors
can dictate a price they are willing to pay at a later date and earn income in the meantime.
The put seller has a limited net profit equal to the put premium; however, the downside of this position is
unlimited (see Figure 6). If the security price declines below the exercise price, the put will be exercised
and the put seller will be obligated to purchase the security. Net loss equals the exercise price plus the
premiums received less the current market price.
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Figure 6 — Put Writer Payoff Diagram
Payoff
Exercise Price
Security Price
FACTORS INFLUENCING OPTION PREMIUMS
The fee or premium to be paid to purchase an option can be determined using a variety of quantitative
techniques. One of the most commonly used models is the Black-Scholes options pricing model. The
Black-Scholes model is discussed in further detail in the sequel note An Introduction to Pricing Options
(Ivey Publications).
In general, option pricing models have several inputs. One key determinant is the current market price of
the underlying security. The amount by which an option is in-the-money is referred to as the option’s
intrinsic value (intrinsic value = market price – strike price). The intrinsic value is one component of an
option’s value and the other component is referred to as its time value. The time value equals the option’s
premium less its intrinsic value (time value = premium – intrinsic value). Time value is a function of the
time remaining until expiration together with any restrictions on when exercise may occur, the volatility of
the underlying security’s price, and the effective cost of holding a position in the underlying security,
including prevailing interest rates and dividends to be paid, if applicable.
PUT-CALL PARITY
Logic dictates that any two investment strategies with identical payoffs should cost the same. This
principle, known as the Law of One Price, can be restated as: If the two investments have the same payoffs
at expiration, then they must have the same value today. Based on this principle, a put option can be priced
by knowing the value of a related call option.
The basic relationship that exists between European calls and puts written on the same asset, with the same
exercise price and expiration date, is known as put-call parity. If an investor were to purchase a call and
sell a put on the same underlying security, with identical exercise prices and expiration dates, the resulting
payoff at maturity would be the same as a strategy that consists of borrowing money to purchase the
underlying security.
Value of Call – Value of Put = Underlying Security Price – PV(Exercise Price)
Rearranging this formula yields the basic form of the put-call parity:
Value of Call + PV(Exercise Price) = Value of Put + Underlying Security Price
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Figure 7 — Payoff Diagram of Purchasing a Call and Selling a Put
Payoff
Exercise Price
Security Price
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Exhibit 1
OTHER DERIVATIVE INSTRUMENTS
EMPLOYEE STOCK OPTIONS
Employee stock options (ESOs) are call options on the common stock of a company that issued to
employees as a form of non-cash compensation. A company will issue ESOs to compensate executives and
other employees and to align their interests with the company’s other shareholders. As the company’s
stock price appreciates, the holder of the ESO benefits and thus employees with stock options may be
incentivized to perform and behave in a manner that benefits the company and its publicly traded stock.
ESOs are often issued as unvested, meaning they must be held for a period of time until they can be
exercised. A vesting schedule for issued ESOs outlines the date after which the options may be exercised,
the number of options granted, and the exercise strike price of the issuance. Further, ESOs are usually
contingent on continued employment with the issuing company and termination or departure often results
in the employee forfeiting all or a portion of the issued options.
ESOs differ from standardized, exchange-traded options in that they are issued at zero cost to the recipient
and, with a few exceptions, are non-transferable; thus, they must be exercised by the intended recipient or
allowed to expire. ESOs also tend to have much longer durations than standardized market options; it is not
unusual for an ESO to have a maturity date 10 years from its date of issue.
Another key difference between ESOs and exchange-traded options is that upon exercise of an employee
stock option, the granting company must issue primary shares to the option holder at the predetermined
strike price, resulting in dilution to the existing shareholders. Exchange-traded and OTC options are
contracts between two individual parties without affiliation to the company itself. The exchange-trade or
OTC contract is based on existing shares in the secondary market; thus exercise and transfer do not affect
the overall share count of a company.
RIGHTS AND WARRANTS
Rights and warrants share many similar characteristics with one another and with call options. The holders
of rights, warrants and call options all possess the right to purchase an underlying stock at a stated price
during a specific period or on a specified date. Rights and warrants differ from options in that they are most
often issued by a corporation not by an investor and, similar to ESOs, they require the issuance of primary
stock, resulting in dilution to the company’s other shareholders. Rights and warrants differ from one
another based on their lifespan or time to expiration: rights are short-term instruments with a typical
lifespan of four to six weeks; warrants are long-term instruments with typical lifespan of three to five
years.
Rights are issued in a similar manner to dividends: shareholders receive a pro rata number of rights
certificates proportionate to their ownership in the security. Rights holders typically have the ability to
exercise some or all of their rights, sell some or all of their rights, buy additional rights or do nothing and
allow the rights to expire. Thus, a secondary market may be created where the rights are valued using the
same methodologies as call options, having both intrinsic and time value components.
Rights allow the corporation to raise equity capital in the near-term, and, in particular, rights are useful
during generally unreceptive market conditions because they specifically target those investors who are
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most likely to purchase the stock - that is, the existing shareholders. Further, rights protect shareholders
from dilution by giving them the first opportunity to acquire new shares and maintain their proportionate
interest in the corporation.
Warrants are most commonly issued in connection with new debt or preferred stock offerings. A
corporation uses the warrant as a sweetener, making the offering easier to sell into the market or lowering
the interest rate required to be paid by providing the buyer with the opportunity to participate in potential
capital gains of the corporation’s common stock. Warrants are usually detachable, and thus, similar to
rights, a secondary market may also develop.
SWAPS
Companies and individuals may be subject to unpredictable cash flows due to dynamic variables, such as
interest rates, foreign exchange rates and commodity prices. Cash flow variability and the associated risk
can be mitigated by employing a derivative instrument known as a swap. Acting as a series of forward
contracts, a swap is an agreement between two counterparties to periodically exchange certain cash flows
of one security for cash flows of another up to a specified maturity date. The counterparty in a swap can be
either another individual or a swap dealer.
For instance, in an interest rate swap the two parties enter into a fixed-for-floating agreement whereby the
cash flows of a fixed rate bond are exchanged for those of a floating rate bond. The bonds used in a fixedfor-floating interest rate swap must have the same maturity and principal amount.
In a currency swap, the counterparties exchange cash flows of two different currencies periodically for the
duration of the swap agreement. These cash flows are typically exchanged as the cash flows of par bonds.
For example, in a fixed-for-fixed dollar-euro five-year currency swap, the counterparties lock in the current
exchange rate and receive periodic payments equal to the interest payments on their bond and, at maturity,
receive the principal and interest payment.
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