Financial Derivatives
Fall 2008
Derivatives
A derivative is an obligation to accomplish a transaction in the future. Because the terms are
specified in detail within the contract, the obligation derives its value from the underlying asset
that would be bought or sold to fulfill the contract. Examples of widely-used derivatives include
forward contracts, repurchase agreements, futures contracts, swaps, options, and swaptions.
Derivatives are powerful tools that can be very useful in managing risk, if properly applied, but
devastating if used carelessly or speculatively.
A forward contract is an agreement for purchase, sale, or exchange of a specified asset (such as
a load of wheat or a portfolio of bonds) for delivery at a specified place on a future date.
Payment is made upon delivery at the price specified in the contract. The contract is a firm
obligation, and there may be a deposit required. Buyers have a long position and sellers have a
short position. Forward markets may be self-regulating and operate without organized
exchanges. There are active global forward markets in energy and foreign exchange.
A repurchase agreement is a form of forward contracting that is essentially a secured loan to a
dealer in government securities. The investor buys part of the dealer’s inventory and
simultaneously arranges to sell it back later at a specified higher price. The length of time varies
from a day to several months. There are also “continuing contracts” that are automatically
renewed every day, but can be canceled by either party with as little as one day’s notice. Also,
there are reverse repurchase agreements in which an investor sells securities from its portfolio
to a dealer and agrees buy them back later. Repurchase agreements are sometimes called RPs,
repos, or buybacks.
A futures contract is a form of forward contracting with a formal structure in which the parties
contract with a clearinghouse, instead of each other, post margin money as collateral, and markto-market regularly. Trading takes place on organized exchanges. At the time the contract is
created, no money changes hands between buyer and seller, and the contract itself has zero
market value. Money required on margin is deposited to assure that the contract will be fulfilled,
and any excess is returned upon completion of the contractual obligations. Obligations under a
futures contract generally can be extinguished simply by taking an offsetting position with the
clearinghouse (for example, a trader can close a long position by taking an offsetting short
position with the same underlying asset and delivery date). Indeed, most contracts are “settled
for cash” in this manner.
A swap is an agreement to exchange cash flows in the future, based upon interest rates, equity
returns, currency exchange rates, or some other economic variable. A simple interest rate swap,
for example, may obligate a participant to pay interest at a variable rate and receive interest at a
fixed rate, with the amount defined as a percentage of the notional principal specified in the
contract. Thus a swap is like a series of forward contracts. Like forward markets, swap markets
may be self-regulating and operate without organized exchanges.
An option is an enhanced forward contract that does not require the option holder to fulfill the
contract—it is called an option because the holder may opt out of the agreed action. The option
contract specifies the underlying asset, the exercise price, and the expiration date. An option to
buy the underlying asset is a call option, and an option to sell the underlying asset is a put
option. The holder of a call has the privilege of buying the underlying asset at the specified
exercise price, but would desire to do so only if the exercise price were below the market price.
Likewise, the holder of a put has the privilege of selling the underlying asset at the exercise
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Financial Derivatives
Fall 2008
price, but would desire to do so only if the exercise price were above the market price. Because
of the privilege of opting out of the obligation to buy or sell, an option is more valuable than a
forward contract, and has a positive market value throughout its life. After expiration, however,
it can no longer be used and has no value.
A currency option is an option to exchange one currency for another at a specified exchange
rate. A call option written on the U.S. Dollar in London, for example, gives the holder the
privilege (but not the obligation) of buying U.S. Dollars in exchange for British Pounds at a
specified exchange rate. Likewise, a put option written on the Pound in New York conveys the
privilege of selling Pounds in exchange for Dollars at a specified rate. The twist is that this put
option written in New York is the same thing as the call option written in London, when both
have the same expiration date—and any disparity in prices would present a lucrative but shortlived arbitrage opportunity.
A swaption is an option to enter into, cancel, or extend a swap. The terms of the swap are
established at the time the swaption is written and the holder has the right, but not the obligation,
to fulfill the contract at a later date. A call swaption is an option to enter into a swap that, if
exercised, involves receiving a fixed rate and paying a floating rate. A 5/2 call swaption, for
example, allows the holder to receive fixed and pay variable in a three-year swap that begins two
years later. A put swaption, if exercised, involves entering into a swap to receive a floating rate
and pay a fixed rate.
There are also futures and forward contracts on swaps, which obligate the participants to fulfill
the specified contracts. The terms are like swaptions, but these contracts lack the privilege of
opting out.
Also, there are options on futures and futures on options. An option on a futures contract
allows the holder to buy (in the case of a call) or sell (in the case of a put) a specified futures
contract within a specified time. A futures contract on an option obligates the buyer to purchase
a specified option at a specified time—likewise, the seller of the futures contract is obligated to
sell the specified option.
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Financial Derivatives
Fall 2008
Swaps
Swaps are agreements to exchange cash flows in the future. There are several types of swap,
including interest rate swaps, currency swaps, and equity swaps. Two or more of these basic
swaps can be combined to create a variety of custom swaps.
An interest rate swap is a variation on forward contracting that is structured essentially as a
“loan” in which the party in the swap “lends” a sum to the underwriter and the underwriter
“lends” the same sum back to the party. This sum never really changes hands at all, and
therefore is called the “notional principal” (“notional” in this context means that the principal is
imaginary). Only the subsequent cash flows, calculated the same way as interest payments,
really occur. The underwriter may offset its risk with futures or options, or by arranging an
offsetting swap with a counterparty, as in the illustrations below:
Illustration of a floating-/fixed- rate swap:
Variable
Party
Fixed
Net: fixed – variable
Variable
Underwriter
Fixed
Counterparty
Net: variable – fixed
If net is positive, underwriter pays party, and if net is negative, party pays underwriter.
Example: Suppose the notional principal is $1,000,000, with the party paying LIBOR and
receiving fixed at 6%, with semi-annual payments. Then suppose LIBOR is 6.5% at the time the
first payment is due. The net would be .5% on an annual basis, or .25% with semi-annual
payments. The party would pay the underwriter $2500.
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Financial Derivatives
Fall 2008
Illustration of a floating-to-floating swap:
T-bill
Party
T-bill
LIBOR
Underwriter
Counterparty
LIBOR
As a custom feature, such swaps may include caps, floors, or collars that place limits on the net
payment. For example, the party might negotiate a cap on the T-bill rate paid out, a floor on the
LIBOR rate received, or limits on both (which is a collar). The “price” for the underwriter’s
services could be expressed through explicit fees, or through premia paid by the party and
counterparty over the base variable rate (for example, the party might pay T-bill plus 0.5% and
receive LIBOR, with the counterparty paying LIBOR plus 0.5% and receiving T-bill, thus
netting the underwriter 1% of the notional principal per year).
Currency swaps developed from parallel loans that had become common by the 1960s. For
example, suppose a U.S. parent company wants to make a loan to its German subsidiary, while at
the same time there is a German parent company about to make a loan to its U.S. subsidiary.
They could avoid some of the costs of international transfers by exchanging loan guarantees
between the parents, and then letting the U.S. parent lend money to the U.S. subsidiary while the
German parent lends to the German subsidiary, as illustrated below:
Illustration of a parallel loan:
United States
U.S. Parent
Germany
loan
German Parent
guarantees
Principal
Debt
service
U.S. Subsidiary
of German Firm
Principal
Debt
service
German subsidiary
of U.S. Firm
The net result for the U.S. Parent is that it lends dollars in the U.S. and receives deutschemarks
in Germany through its subsidiary. It then pays debt service in deutschemarks at German
interest rates, and receives debt service in dollars at U.S. rates. At the maturity of the loan, it
repays the principal in deutschemarks and receives the principal in dollars.
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Financial Derivatives
Fall 2008
In a straight currency swap, two companies borrow in their own countries and agree to pay each
others’ debt obligations. For example, suppose a U.S. company needs to borrow German Marks,
and a German company needs to borrow U.S. Dollars.
Illustration of a straight currency swap:
For purposes of illustration, suppose the current exchange rate is €1 = $1.50, principal is
$1,500,000; and instead of borrowing in foreign markets each company takes a domestic loan
while arranging a currency swap:
Illustration of a straight currency swap
$1,500,000
$1,500,000
1
1
German rate x €1,000,000
German rate x €1,000,000
2
U.S. rate x $1,500,000
€ 1,000,000
2
U.S. rate x $1,500,000
Borrow in
Europe,
invest in US
€ 1,000,000
3
3
$1,500,000
German Company
€ 1,000,000
Intermediary
U.S. Company
Borrow in
US, invest
in Europe
€ 1,000,000
$1,500,000
Step 1 is notional
Steps 2 & 3 are net
1.
2.
3.
Initial exchange of principal is notional, because net is zero. Amounts reflect prevailing
spot exchange rate.
Periodic payments are handled as net amounts, based on current exchange rates.
Final exchange of principal will be done at an exchange rate agreed to in the swap
arrangement. The actual payments are the net amounts, based upon the current exchange
rate at the time of payment. For example, if the dollar weakened and the exchange rate were
$1 = DM1.45, the U.S. company would pay DM 50,000, and the German company would
receive DM 50,000.
Currency/interest rate swaps can be created by combining straight currency swaps with interest
rate swaps.
In an equity return swap, the party pays a fixed or variable interest rate, and receives the rate of
return on a chosen equity index. Available indices include the S&P 500, S&P 100, MMI, plus
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Financial Derivatives
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various Japanese, European, and Latin American stock market indices. Custom indices and
individual stocks are also available.
Illustration of an equity return swap:
Equity Index
Return*
Investor
Underwriter
Libor ± Spread
*Equity index return includes dividends, paid out
quarterly or reinvested
In an equity asset allocation swap, the party trades the returns on one equity index for the
returns on another equity index. Available indices include the S&P 500, S&P 100, MMI, plus
various Japanese, European, and Latin American stock market indices. Custom indices and
individual stocks are also available.
Illustration of an equity asset allocation swap:
Foreign equity index
Return* A
Investor
Underwriter
Foreign equity index
Return* B
*
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Financial Derivatives
Fall 2008
In an equity call swap, the party pays a fixed or variable interest rate periodically through the life
of the swap, and receives the rate of appreciation on a chosen equity index at maturity of the
swap. If the index drops, the investor receives nothing, but pays only the interest component of
the swap. If the index rises, the maturity payment is based on the percentage increase in the
index from the start of the swap until the maturity (for example, if the index increased from 100
to 110, the maturity payment to the investor would be 10% of the notional principal). Available
indices include the S&P 500, S&P 100, MMI, plus various Japanese, European, and Latin
American stock market indices. Custom indices and individual stocks are also available.
Illustration of an equity call swap:
Equity Index Price
Appreciation*
Investor
Underwriter
Libor ± Spread
* No depreciation—settlement at maturity
In an equity asset swap, the party receives the rate of return on a chosen equity index, while
paying the returns generated by a specified pool of assets (such as a bond portfolio or
commercial real estate). Available indices include the S&P 500, S&P 100, MMI, plus various
Japanese, European, and Latin American stock market indices. Custom indices and individual
stocks are also available.
Illustration of an equity asset swap:
Asset
Equity Index
Return*
Investor
Underwriter
Coupon
*Includes dividends, paid quarterly or reinvested
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