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INTRODUCTION TO
DERIVATIVE SECURITIES
ECI RISK TRAINING
www.ecirisktraining.com
Alan Anderson, Ph.D.
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DERIVATIVE SECURITIES
A derivative security is a contract
whose value is based on (derived
from) an underlying financial asset
Derivatives are widely used as
hedging instruments due to their
flexibility
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Derivative securities are traded on
organized exchanges, such as the
Chicago Mercantile Exchange (CME)
They are also traded directly
between counterparties in the
“over-the-counter” (OTC) market
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The basic categories of
derivative securities are:
forward contracts
futures contracts
swaps
options
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FORWARD CONTRACTS
A forward contract is an agreement between
two counterparties to exchange an asset at an
agreed-upon price at a specified point in the
future
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For example, suppose that a U.S. importer
needs to buy £100,000 in six months
In order to hedge the risk that the dollar will
depreciate against the pound in six months,
which would increase the dollar price of the
pounds, the importer can enter into a forward
contract with a bank in which:
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the importer agrees to buy £100,000 from
the bank at a fixed price in six months
(this is known as a long forward position)
the bank agrees to sell £100,000 to the
importer at a fixed price in six months
(this is known as a short forward position)
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Suppose that the fixed price, known as the
delivery price, is $1.60/£. This means that in
six months, the importer will pay $160,000
for the £100,000 regardless of the exchange
rate that prevails at that time
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In six months, if the dollar has depreciated
(i.e., the exchange rate has risen), the
importer will save by buying pounds
through the forward contract
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In six months, if the dollar has appreciated
(i.e., the exchange rate has fallen), the
importer will pay a higher price by buying
pounds through the forward contract, but
will have eliminated all uncertainty over the
cost of the pounds
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The advantage to hedging with a forward
contract is that the contract can be
customized to the needs of the hedger
The counterparties can agree to any
underlying asset and any delivery time
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The disadvantage is that the hedger cannot
benefit from changes in the risk factor being
hedged
For example, if an importer hedges against the
risk of a depreciating dollar with a forward
contract, he does not save if the dollar
appreciates
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FUTURES CONTRACTS
A futures contract is similar to a forward
contract; the main differences are:
futures contracts are traded on organized
exchanges, while forward contracts are
traded in the over-the-counter market
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futures contracts are not subject to
counterparty risk, since the derivatives
exchanges guarantee their performance;
forward contracts are subject to default
risk
futures contracts can easily be unwound
(offset), while forward contracts cannot
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futures contracts are “marked-to-market”;
this requires an initial deposit in a margin
account, and may require further funding
throughout the lifetime of the contract
forward contracts are not marked-to-
market
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SWAPS
A swap is an agreement between two
counterparties to exchange cash flows at
regular intervals based on the difference
between two variables, such as interest
rates or exchange rates
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EXAMPLE
Suppose a firm has issued floating-rate debt
that pays LIBOR (the London Interbank Offer
Rate) to bondholders and wishes to hedge the
risk that interest rates will rise in the future
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The firm can enter into an interest rate
swap with a swap dealer in which it
agrees that every six months, it will:
receive LIBOR from the dealer
pay a fixed rate of interest to the
dealer
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This arrangement has the effect of
transforming the firm’s floating-rate
liability into a fixed-rate liability
Suppose that the fixed rate is 5%; the
relevant cash flows are shown in the
following diagram:
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This diagram shows that the firm will
use the LIBOR payments from the swap
dealer to pay its bondholders; the 5%
that the firm pays to the swap dealer
now represents its interest rate costs
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The firm now pays 5% each year instead
of an unknown floating rate of interest
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OPTIONS
An option gives the buyer the right,
but not the obligation, to buy or sell
an asset in the future at a fixed
price; the fixed price is known as the
strike price or exercise price
Options are traded on exchanges and
in the over-the-counter market
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OPTIONS CLASSIFICATION
Call option: provides the right to buy an asset
Put option: provides the right to sell an asset
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European option: can be exercised
only on its maturity date
American option: can be exercised
at any time prior to maturity
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THE BASIC PROPERTIES
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OF CALL OPTIONS
The payoff to a call option is:
MAX (S-X, 0)
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where:
MAX = maximum
S = price of underlying asset
X = strike (exercise) price
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How is this payoff determined? Suppose that
an investor owns a call option with strike
price X. On the option’s maturity date, the
market price of the underlying asset is S.
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If S exceeds X, the option will be exercised;
the investor will be able to buy the asset at
a price of X and resell it at a price of S, for
a payoff of S – X
If S is less than or equal to X, the investor
will not exercise the option; its payoff is
therefore 0
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In the first scenario, the payoff is S-X, which
is a positive number. In the second scenario,
the payoff is 0. Therefore, the payoff is the
greater of S-X and 0, which is expressed as:
MAX(S – X, 0)
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PROFIT/LOSS
An option will be exercised as
long as the payoff is positive.
Whether the investor earns a
profit or loss depends on the
price paid for the option.
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For the owner of the call option,
the profit or loss will be:
PAYOFF – PRICE
= MAX(S – X,0) – C
where: C = call price
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PROFIT/LOSS DIAGRAMS
The profits and losses to this option
are shown in the following table and
diagram:
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NOTE
The maximum loss per share
equals the call price of $3;
this occurs for all S ≤ X
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For all S > X, the investor’s profit per share
increases by $1 for each $1 increase in S;
therefore, there is no maximum profit
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TERMINOLOGY
When S > X, a call is in the money
When S = X, a call is at the money
When S < X, a call is out of the money
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THE BASIC PROPERTIES
OF PUT OPTIONS
The payoff to a put option is defined as:
MAX (X - S, 0)
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where:
MAX = maximum
S = price of underlying asset
X = strike (exercise) price
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How is this payoff determined? Suppose
that an investor owns a put option with
strike price X. On the option’s maturity
date, the market price of the underlying
asset is S.
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If S is less than or equal to X, the option
will be exercised; the investor will be
able to buy the asset at a price of S and
sell the asset at a price of X, for a payoff
of X – S
If S exceeds X, the option will be not
exercised; its payoff is therefore 0
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In the first scenario, the payoff is X - S, which
is a positive number. In the second scenario,
the payoff is 0. Therefore, the payoff is the
greater of X-S and 0, which is expressed as:
MAX(X – S, 0)
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Payoff to IBM Put Option 51
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20
15
Payoff ($)
10
5
0
30 35 40 45 50 55 60 65 70 75
Stock Price ($)
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PROFIT/LOSS
An option will be exercised as
long as the payoff is positive.
Whether the investor earns a
profit or loss depends on the
price paid for the option.
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For the owner of the put option,
the profit or loss will be:
PAYOFF – PRICE
= MAX(X – S,0) – P
where: P = put price
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PROFIT/LOSS DIAGRAMS
The profits/losses to this option
are shown in the following table
and diagram:
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Profit/Loss to IBM Put Option 56
20
15
10
Profit/Loss ($)
5
0
30 35 40 45 50 55 60 65 70 75
-5
Stock Price ($)
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NOTE
The maximum loss per share
equals the put premium of $2;
this occurs for all S ≥ X
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For all S < X, the investor’s profit per share
increases by $1 for each $1 decrease in S;
profit reaches a maximum of $X only in the
unlikely event that S falls to zero
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TERMINOLOGY
When S < X, a put is in the money
When S = X, a put is at the money
When S > X, a put is out of the money
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HEDGING WITH OPTIONS
If a hedger needs to buy an asset in the future,
the risk of rising future prices can be hedged
with a call option
If the price of the underlying asset rises above
the option’s strike price, the hedger can buy
the asset at the strike price; if not, the hedger
can buy the asset at the lower market price
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If a hedger needs to sell an asset in the future,
the risk of falling future prices can be hedged
with a put option
If the price of the underlying asset falls below
the option’s strike price, the hedger can sell the
asset at the strike price; if not, the hedger can
sell the asset at the higher market price
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EXAMPLE
Suppose that a jewelry manufacturer
needs to buy silver in six months. The
manufacturer faces the risk that the
price of silver will rise in six months.
In order to hedge this risk, the
manufacturer buys a call option on
silver. Assume that the strike price of
the option is $5/ounce.
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In six months, there are two possible
scenarios:
1) the market price is greater than $5
In this case, the manufacturer exercises
the option and buys silver at $5
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2) the market price is less than or
equal to $5
In this case, the manufacturer
does not exercise the option and
buys silver at the market price
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The manufacturer has set a limit on the
price that it will pay for silver in six
months ($5) while retaining the ability
to pay a lower price
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EXAMPLE
Suppose that an oil company will sell crude
oil in three months. The oil company faces
the risk that the price of oil will fall in
three months.
In order to hedge this risk, the oil company
buys a put option on oil. Assume that the
strike price of the option is $50/barrel.
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In three months, there are two possible
scenarios:
1) the market price is greater than $50
In this case, the oil company does not
exercise the option and sells oil at the
market price
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2) the market price is less than or equal
to $50
In this case, the oil company exercises
the option and sells oil at the strike
price of $50
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The oil has set a minimum price at which
it will be able to sell its oil ($50) while
retaining the ability to sell the oil at a
higher price
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HEDGING WITH FORWARD
CONTRACTS VS. OPTIONS
The advantage to hedging with forward
contracts is that there is no cost to the
hedger
The disadvantage is that the hedger locks in
a specific price, and cannot benefit from
favorable movements in market prices
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The advantage to hedging with options is
the ability to benefit from favorable
market movements in market prices while
guaranteeing a maximum price at which
an asset can be bought or a minimum
price at which it can be sold
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The disadvantage to hedging with
options is that the hedger must pay
a price to buy an option
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