Introduction to Derivatives
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Course Objectives
Understand what a Explain a forward Explain a futures
derivative contract is contract contract
Understand option Outline the components
contracts of a swap contracts
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Derivative Contracts
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What is a Derivative Market?
Markets are used to transfer goods, services, funds, or risks.
Derivative market is a market developed over time to transfer risk from one party to another.
Risk Risk
Company A Derivative Market Company B
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What is a Derivative Contract?
A derivative contract derives its value from an underlying asset such as a stock, currency, or
commodity, hence the name derivative.
Underlying
Asset
Risk Risk
Counterparty Derivative Counterparty
A Contract B
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Components of a Derivative Contract
Derivative contracts will generally include these important components:
An Underlying Counterparties with Long / An Expiration or
Asset Short Positions Maturity Date
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Derivative Contract Underlying Assets
A derivative contract will derive its value based on the dynamic value of an underlying asset. A
few common underlying assets are:
Stocks Bonds Currencies Commodities Market Indices Interest Rates
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Long Position and Short Position
In a derivative contract, one party is often described as holding a long position while the
other holds a short position.
Long Position Short Position
Counterparty A Counterparty B
Benefits when the value of Benefits when the value of
the underlying asset the underlying asset
increases decreases
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Derivative Contract Expiration/Maturity Date
Derivative contracts will also include an expiration or maturity date. This is the date when the contract
agreement ends and any differences in the two positions are finally settled.
Derivatives will also specify delivery type at expiration when applicable:
VS
Cash-Settled
Physical Delivery
Cash-settled means that
Physical delivery means that
differences in the
at the expiration date, the
counterparties’ positions will
quantity of the underlying
be settled in cash rather
asset specified in the contract
than delivering the
will be delivered to buyer.
underlying asset.
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Over-the-Counter vs. Exchange-Traded
Derivative contracts can be traded either over the counter, or through exchanges.
Over-the-Counter
Customized contracts made
through a broker-dealer, or
VS Exchange-Traded
Standardized contracts that
are freely traded on a
directly between the two formal, organized exchange.
counterparties.
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Uses of Derivatives Contracts
Derivatives are generally used for two purposes: hedging and speculating.
Hedging
Hedging involves protecting a
current financial position
VS Speculating
Speculating involves trying to
make guesses about the
from potential losses. direction of the underlying
asset’s value to make a
profit.
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Types of Derivative Contracts
Common derivative contracts include forwards, futures, options, and swaps.
Forward Commitment Contingent Claims
Forwards Futures Swaps Options
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Forward Contracts
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What is a Forward Contract?
A forward contract is an agreement between two parties to exchange an asset for a pre-
specified price on a specific date in the future. Examples include:
Example 1
In one year’s time Party A will purchase 8,000 barrels of oil from Party B at $50 per barrel.
8,000 barrels of oil
$40,000 USD
Party A Party B
Example 2
In one month’s time Party A will purchase $500,000 USD from Party B for $675,000 CAD.
Example 3
In five year’s time Party A will purchase 600 troy ounces of gold from Party B for $900,000 USD.
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What is the Purpose of a Forward Contract?
Forwards are over-the-counter contracts. Although they can be used for speculating, the customizability
makes forwards very useful for hedging.
Hedging
VS Speculating
For example, industries that heavily rely on a commodity such as an airline on jet fuel, can hedge the
price of fuel using forwards to reduce volatile prices.
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Components of a Forward Contract
Important components of a forward contract will include:
1. Underlying Asset 2. Delivery Date 3. Specified Price
4. Quantity 5. Type of Delivery
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Forward Contract Profit/Loss (Pay-off) Diagrams
At expiration, a long position benefits the higher the price of the underlying asset. A
short position benefits the lower the price of the underlying asset.
Forward Contract Long Position Forward Contract Short Position
Profit/Loss
Profit/Loss
K Underlying Asset Price K Underlying Asset Price
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Forward Contract – Worked Example
Let’s consider a situation involving a forward contract.
Read the following scenario:
• A party needs 10,000 barrels of oil in 3 months.
• They are worried about the price of oil rising, so they enter
into a forward contract to purchase 10,000 barrels at
$50/barrel in 3 months time.
• At expiration, the spot price of oil is $55/barrel.
• How much money was saved from entering into the forward
contract?
• What if the spot price had instead dropped to $40?
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Forward Contract – Worked Example
Let’s consider a situation involving a forward contract.
Read the following scenario:
A party needs 10,000 barrels of oil in 3 months. They are
worried about the price of oil rising, so they enter into a
forward contract to purchase 10,000 barrels at $50/barrel
in 3 months time. At expiration, the spot price of oil is
$55/barrel. How much money was saved from entering
into the forward contract? What if the spot price had
instead dropped to $40?
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Futures Contracts
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What is a Futures Contract?
A futures contract is similar to a forward contract. It is an agreement to exchange an
underlying asset for a pre-specified price at a specified date in the future.
The major differences however include:
01 Futures contracts have standardized contract terms.
02 Futures contracts are traded on exchanges rather than
over the counter.
03 Futures contracts involve margins.
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What is the Purpose of a Futures Contract?
Futures contracts are often used for hedging, however the liquidity of futures contracts and the ability
to leverage through margins makes futures attractive for speculating.
Hedging
VS Speculating
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Components of a Futures Contract
A futures contract will generally have the following important components:
1. Underlying Asset 2. Delivery Date 3. Specified Price 4. Contract Size
5. Type of Delivery 6. Tick Size 7. Initial and
Maintenance Margin
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Futures Contract Profit/Loss (Pay-off) Diagrams
Similar to a forward contract, a long position benefits the higher the price of the underlying asset.
A short position benefits the lower the price of the underlying asset.
Futures Contract Long Position Futures Contract Short Position
Profit/Loss
Profit/Loss
K Underlying Asset Price K Underlying Asset Price
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Futures Contract Example
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Futures Contract Example
Delivery Date
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Futures Contract Example
Contract Size
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Futures Contract Example
Tick Size
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Futures Contract Example
Price
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Futures Contract Example
Margins
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Mechanics of the Exchange - Margins
A major difference between forwards and futures is that futures contracts are settled daily.
A counterparty’s margin account is credited or debited as the spot price of the underlying asset
changes.
Counterparty A Margin Call Counterparty B
If the margin account of the buyer or seller falls below a certain point, known as the minimum
required margin or secondary margin, a margin call will happen. The counterparty is required to
deposit more money into the margin account to retain their position.
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Futures Contract – Worked Example
We are going to calculate the margin requirements for
the following contract:
Oil Futures Contract
Deliver Date 3 days from now
Futures Price $50.00 USD per barrel
Contract Size 1,000 barrels
Tick $0.01
Tick Value $10
Settlement Physical Delivery
Initial Margin $5,000 The amount needed to deposit
Maintenance Margin $3,000 Minimum balance required
Number of Contracts 10
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Futures Contract – Worked Example
Exposure: $50/bbl x 1,000 bbls x 10 contracts = $500,000 Tick: $0.01 per barrel
Initial Margin: $5,000 x 10 contracts = $50,000 Tick Value: 1,000 x $0.01 x 10 contracts = $100
Maintenance Margin: $3,000 x 10 contracts = $30,000
Day 1 Day 2 Day 3 (Expiration)
Settlement Price $51.10/barrel $47.50/barrel $50.20/barrel
Beginning Margin Account $50,000 $61,000 $50,000
Tick Movement 110 -360 270
Change to Margin Account +$11,000 -$36,000 +$27,000
Total Before Margin Call $61,000 $25,000 $77,000
Margin Call $0 $25,000 Margin Call 0
Ending Margin Account $61,000 $50,000 $77,000
Deposited Amount $50,000 $75,000 $75,000
Net Gain(Loss) $11,000 -$25,000 $2,000
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Futures Contract – Worked Example
We are going to calculate the margin requirements for the
following contract:
Oil Futures Contract
Deliver Date 3 days from now
Futures Price $50.00 USD per barrel
Contract Size 1,000 barrels
Tick $0.01
Tick Value $10
Settlement Physical Delivery
Initial Margin $5,000
Maintenance Margin $3,000
Number of Contracts 10
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How are Futures Prices Calculated?
Imagine that you plan to buy 1,000 barrels of oil in 1 year’s time. There are two strategies
you can consider:
Strategy 1: Buy Now and Hold Strategy 2: Buy a Futures Contract
You could borrow money to buy the 1,000 You could buy the futures contracts for 1,000
barrels of oil at the spot price and hold it for barrels of oil with an expiration in one year’s
one year. At the one-year mark you would pay time. The cost in this scenario would simply
back the amount and any interest. be the cost of the futures contract.
Cost = Spot Price + Carry Cost (Interest + Cost = Futures Contract Price
Storage) – Carry Return
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How are Futures Prices Calculated?
Let’s assume the spot price is $50/barrel, the cost of borrowing is 5%, and the cost of
storing 1,000 barrels of oil is $2,000. Let’s also assume a 1-year futures contract is priced at
$55/barrel (or $55,000 per contract).
Strategy 1: Buy Now and Hold Strategy 2: Buy a Futures Contract
Cost = Spot Price + Carry Cost (Interest + Cost = Futures Contract Price
Storage) – Carry Return
Cost = $50 x 1,000 + ($50 x 1,000) x 5% + $2,000 - $0 Cost = $55,000
Cost = $54,500
If this were the case, what could an investor do to profit from this situation?
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How are Futures Prices Calculated?
If the spot price and futures price are not in equilibrium, there is an arbitrage opportunity:
Action Cash Position
Strategy 1: Buy Now and Hold
Borrow $50,000 +50,000
Cost = $54,500
Buy 1,000 barrels of oil at the spot price -50,000
Pay interest and storage costs -4,500
Sell a futures contract for 1,000 barrels +55,000
Repay the loan -50,000
Total +$500
Strategy 2: Sell a Futures Contract
Cost = $55,000
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Options
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What is an Option?
An option contract gives one party the right, but not obligation, to buy or sell an underlying asset at a
specific price by or at a specific date.
If the party that has the right to buy or sell chooses to exercise their option, the counterparty to the
contract must deliver. The two basic options include:
Call Option
A call option is the option to
buy an underlying asset at a
VS Put Option
A put option is the option to
sell an underlying asset at a
specified price in the future. specified price in the future.
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What is the Purpose of an Option?
Options are used for both hedging and speculating purposes.
Since options give the right but not obligation to exercise, investors can use options to
speculate while also reducing downside losses.
Long and short positions on calls and puts can be combined in many different ways to serve
different purposes.
Hedging
VS Speculating
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Option Examples
Let’s look at examples of both types of options:
Put Option
Call Option
The right to sell 600 troy ounces of
The right to buy 1,000 barrels of oil at
gold for $1,500 per troy ounce in 6
$50 per barrel in one year’s time.
month.
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Components of an Option Contract
Important components of an option will include:
1. Underlying Asset 2. Expiration Date 3. Strike Price 4. Contract Size
5. Type of Delivery 6. Option Premium 7. American vs. European
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Bloomberg Call Option Example
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Bloomberg Call Option Example
Stock Price
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Bloomberg Call Option Example
Ticker
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Bloomberg Call Option Example
Strike Price
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Bloomberg Call Option Example
Exercise Type
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Bloomberg Call Option Example
Contract Size
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Bloomberg Call Option Example
Delta
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Bloomberg Put Option Example
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Bloomberg Put Option Example
Stock Price
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Bloomberg Put Option Example
Ticker
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Bloomberg Put Option Example
Strike Price
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Bloomberg Put Option Example
Exercise Type
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Bloomberg Put Option Example
Delta
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Call Option Profit/Loss (Pay-off) Diagrams
Here we can see the profit/loss diagrams for a long position and short position on a call option.
Short Call Position
Long Call Position
$55
Profit/Loss
Profit/Loss
Profit = $5 - $1 = $4 $1 Loss = $1 - $5 = -$4
K
-$1 Underlying Asset K Underlying Asset
Spot Price Spot Price
$50 $55 $50
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Put Option Profit/Loss (Pay-off) Diagrams
Here we can see the profit/loss diagrams for a long position and short position on a put option.
Short Put Position
Long Put Position
$45 Loss = $1 - $5 = -$4
Profit/Loss
Profit/Loss
Profit = $5 - $1 = $4 $1
K
-$1 Underlying Asset K Underlying Asset
$45 $50 Spot Price $50 Spot Price
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Moneyness
Moneyness refers to whether an option has intrinsic value by comparing the strike and spot prices.
Call Option Put Option
At-the-Money At-the-Money
Out-of-the- In-the- In-the- Out-of-the
Money Money Money Money
Underlying Asset Underlying Asset
Profit/Loss
Profit/Loss
K Spot Price K Spot Price
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Options – Worked Example
Let’s consider a situation involving the use of an option.
Read the following scenario:
• An investor holds 100 shares of Company A, which is currently
trading at $50 per share.
• They believe the stock price will fall soon, and to hedge this risk
they decide to purchase 100 put options on Company A’s shares.
• These put options have a strike price of $45 and a premium of $2.
• What is the investor’s profit or loss in the following three scenarios:
o Scenario 1 – if the stock falls to $45.
o Scenario 2 – if the stock falls to $40.
o Scenario 3 – if the stock falls to $0.
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Options – Worked Example
The table shows the scenarios where the spot price is $45, $40 and $0.
• Put option premium - $2 per share x 100 shares = $200.
• Original spot price is $50 per share and the strike price is $45 per share.
Spot price = $45 Spot price = $40 Spot price = $0
Gain/Loss on Stock -$500 -$1,000 -$5,000
Premium -$200 -$200 -$200
Gain/Loss on Put Option $0 $500 $4500
Net Gain/Loss -$700 -$700 -$700
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Options – Worked Example
Let’s consider a situation involving the use of an option.
Read the following scenario:
• An investor holds 100 shares of Company A, which is currently
trading at $50 per share.
• They believe the stock price will fall soon, and to hedge this risk
they decide to purchase 100 put options on Company A’s shares.
• These put options have a strike price of $45 and a premium of $2.
• What is the investor’s profit or loss in the following three scenarios:
• Scenario 1 – if the stock falls to $45.
• Scenario 2 – if the stock falls to $40.
• Scenario 3 – if the stock falls to $0.
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Swap Contracts
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What is a Swap Contract?
A swap contract is a derivative in which two counterparties exchange cash flows (known as
“legs”) over a period of time. Often one leg will be a fixed payment, while the other will be a
floating payment.
Fixed
January 1, 2020
Floating
Fixed
June 1, 2020
Floating
Fixed
January 1, 2021 (Expiration)
Floating
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Components of a Swap Contract
The major components of a swap contract include:
1. Underlying Asset 2. Notional Amount 3. Maturity Date
4. Fixed / Floating Rates 5. Payment Frequency
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Interest Rate Swap
An interest rate swap “swaps” a fixed rate of interest for a floating rate of interest.
• Two counterparties enter into an
interest rate swap with one
counterparty paying fixed while the
Fixed Amount other counterparty pays floating.
• The amount of these payments will be
calculated using fixed and floating
Floating Amount interest rates and a notional amount
Counterparty Counterparty that is not swapped.
A B
• Interest rate swaps are often done to
take advantage of different
comparative borrowing rate
advantages of the two counterparties.
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Interest Rate Swap Example
Let us now add some numbers to the previous example to see how this works.
• Company A and Company B agree to swap fixed for floating interest
rates on a notional value of $1MM.
• The term of the interest rate swap is two years.
• Interest payments will be swapped every six months.
• The fixed rate on the swap is 5.25%.
• The floating rates on the swap (assuming we are looking back) are:
6-Month LIBOR
Now 5.00%
6-months from now 5.20%
12-months from now 5.30%
18-months from now 5.40%
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Interest Rate Swap Example
• Company A and Company B agree to swap fixed for floating interest
rates on a notional value of $1MM.
• The term of the interest rate swap is two years.
• Interest payments will be swapped every six months.
• The fixed rate on the swap is 5.25%.
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Interest Rate Swap Benefits Example
Let’s look at an example of two companies entering into a swap agreement.
Let’s say two companies can borrow at these rates:
Company Fixed Floating
A 5.00% LIBOR
B 6.00% LIBOR + 0.50%
Assume:
• Company A wants to borrow at a floating rate.
• Company B wants to borrow at a fixed rate.
How can the two companies set up a swap contract
that is mutually beneficial?
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Interest Rate Swap Benefits Example
Company A has a comparative advantage against Company B’s borrowing rate, therefore a
mutually beneficial swap can be arranged:
01 Company A will borrow at their fixed rate of 5% and Company B will borrow at their floating rate of
LIBOR + 0.5%.
02 Company A will pay Company B LIBOR on a pre-determined notional amount.
03 Company B will pay Company A a fixed rate of 5.25% on the same pre-determined notional amount.
04 Company A and B will each reduce their costs of borrowing by 25 basis points.
LIBOR
5% LIBOR + 0.5%
5.25%
Lender Company A Company B Lender
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Interest Rate Swap Benefits Example
This swap is mutually beneficial to both counterparties.
Company A Company B
Initial Borrowing Cost 5.00% LIBOR + 0.50%
Amount Paid in Swap LIBOR 5.25%
Amount received in Swap 5.25% LIBOR
Net Borrowing Cost 5.00% + LIBOR – 5.25% = LIBOR + 0.50% + 5.25% - LIBOR =
LIBOR – 0.25% 5.75%
Original Borrowing Cost LIBOR 6.00%
Savings 0.25% 0.25%
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