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Lecture 1 Personal notes with examples
Derivatives 1 (Monash University)
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Lecture 1
Table of Contents
What is a derivative?
What is the underlying variable?
Types of derivative we will talk about
Forward contract
Parties to a Forward contract
Example of a long position
Possible scenarios after 3 months
Pay off diagrams for forward contracts
Long forward contract
Pay off function:
Short forward contract
Pay off function:
Futures contract
Pay off diagrams
Marking to market
What things are standardized?
What happens at the end of a forward/futures contract?
What is a derivative?
A derivative is a financial instrument whose value depends on the value of a
underlying variable.
What is the underlying variable?
Very often the variables underlying derivatives are the prices of traded assets.
A stock option, for
example, is a derivative whose value is dependent on the price of a stock.
Types of derivative we will talk about
Forward contract
Futures contract
Options
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Forward contract
A forward contract is an agreement to either buy or sell an asset at a
specified price on a specified future date (as opposed to buying it right now).
e.g. a forward contract to buy gold in December 2021 at USD 1950 per ounce.
This contract obligates me to buy gold in December 2021 at USD 1950 per
ounce. You can sort of think how this contract might become
favorable/unfavorable to me depending on the price of gold in December 2021.
If the price of gold in December 2021 is less than $1950, I would have to buy
gold at a price higher than the market (I don't want this). If instead the price of
gold is higher than $1950, I can buy gold at a price lower than the market and
then immediately sell it at the market price to net the difference.
Parties to a Forward contract
Every transaction has two parties. If someone is buying, someone else has to
be selling. Same principal applies here.
Long position: the person who agreed to BUY the asset
Short position: the person who agreed to SELL the asset
Example of a long position
I think gold will go up in price sometime in the next 3 months. I go to my broker
and get this deal:
Forward contract to buy 1000 ounce gold @ USD 500 per ounce in 3 months
time.
Possible scenarios after 3 months
Price of gold > $500
I use my contract to buy 1000 oz
gold at $500/oz
I immediately go to the market
and sell the gold I bought at a
higher price
I make a profit
Price of gold < $500
I use my contract to buy 1000 oz
gold at $500/oz (even though I
don't want to, because I would
rather buy it from the market at a
lower price)
I sell the gold I bought at a lower
price (assuming I think price of
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gold might go down further, so
better to sell it and cut losses)
I make a loss
Pay off diagrams for forward contracts
Think about this: if the price of the underlying asset goes up, would you make a
profit or loss?
If you make a profit → the diagram is a upward sloped line
If you make a loss → the diagram is a downward sloped line
Long forward contract
The contract obliges you to buy something at a future date. If the price of thing
goes higher than the price you agreed to buy it at, you can buy it at lower price
and sell it at a higher price. So you make profit when price goes up → upward
sloped line
Pay off function:
Remember: Payoff function is always What you're getting - what you're giving)
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In this case you're getting the current market price and you're paying the
forward price that you previously agreed on.
So, payoff function for a long forward contract = ST
−F
where St is spot price/market price at the future date and F is the forward
price
Short forward contract
The contract obliges you to sell something at a future date. If the price of the
thing goes up before that date, you need to buy the thing from market at a
higher price then sell it to the counter party at a lower price. So you make a
loss when price goes up → downward sloping line
This is assuming you did not own the thing in the beginning. If you already
owned the thing, you would not enter a forward contract because the benefit
of forward contracts is that you don't have to own something to agree to sell it
(also a reason why it's so risky).
Pay off function:
Remember: Payoff function is always What you're getting - what you're giving)
In this case you're getting the forward price you previously agreed on from the
counterparty and you're paying the current market price to buy the thing.
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So, payoff function for a long forward contract = F
− ST
where St is spot price/market price at the future date and F is the forward
price
Futures contract
Like forward contracts, futures contracts involve the agreement to buy and sell
an asset at a specific price at a future date. The futures contract, however, has
some differences from the forward contract.
Futures contracts trade on organised exchanges.
There is no risk of default.
Futures contracts are highly standardised.
Futures contracts are “marked to the market” on a daily basis.
Futures contracts are often cash settled, with no physical delivery
of the underlying asset.
Pay off diagrams
Same as forward contracts. But the reason these F open and F close instead of
F and spot price is that at expiry the forward/future price of a contract is the
same as the spot price. We will get into why this is in week 3
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Marking to market
When you open a futures position (irrespective of whether you go long or
short), you must lodge an initial margin (i.e., a deposit) with the exchange.
At the end of each day, the exchange calculates whether you have made or
lost money today (i.e., mark you to the market). Gains (losses) are added to
(subtracted from) your account.
If your balance gets too low, the exchange makes a margin call (i.e.,
requires you to deposit more funds).
What things are standardized?
The specific terms of a futures contracts are highly standardized
with respect to:
Underlying asset: precisely what asset must be delivered and what its
quality must be.
Contract size: the amount of the underlying asset that has to be delivered
under one contract.
Delivery date: which months the contract expires in.
Delivery arrangements: if physical delivery is possible, exactly the
underlying asset must be delivered.
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What happens at the end of a
forward/futures contract?
All futures contracts can be “closed-out” prior to expiry.
Closing out a futures position simply means entering a new futures position
equal in magnitude but opposite in direction to your original futures position:
If your opening futures positions was long, you close it out by entering a
short position in the same futures contract.
If your opening futures positions was short, you close it out by entering a
long position in the same futures contract
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