Derivative
An instrument whose value depends on, or is derived from, the value of another underlying asset. E.g. futures,
forwards, swaps, options. Derivatives is intangible and expires (maturity). Derivatives play a key role in
transferring risks.
Financial transactions can have embedded derivatives (e.g. structured products). The underlying assets include
stocks, currencies, IR, commodities, weather – we can have derivatives whose underlying asset is interest rates.
Derivatives are traded in an exchange (dealing in standardised asset, so they’re telling you the maturity, strike
price, specific sizes of contract) or over-the-counter (more tailormade, you specify your needs of size, maturity
and price).
Derivatives are used for to hedge risks, to speculate (take a view on the future direction of the market and trade
on it to benefit), and arbitragers (in any state of the world, they will either break even or make money – it is a
no risk strategy, and trading two identical assets are priced differently -> profit).
Forward contracts
A forward contract is an agreement to buy or sell an asset at a certain future time (expiration, maturity) for a
certain, predetermined price (delivery price).
A spot contract is an agreement to buy or sell an asset today.
Long position: party has agreed to buy (ask/offer price). Short position: party has agreed to sell (bid price). Bid
ask spread is difference between the two prices – market maker profit for conducting the trade.
Example:
Possible outcomes:
- Higher exchange rate: you make money – you’ve
settled to a lower price than what is on the market.
- Lower exchange rate: you lose money – you’ve
agreed to pay a price that is too high than reality
, If future exchange rate is exactly the forward
contract price, then it will breakeven. If it is higher,
it will make a profit (difference between two prices)
and if it is lower, it will make a loss (difference
between two prices).
Shorting a forward contract: you are in it to sell and
not to buy.
If price is higher in the future, you lose money as
you’ve agreed to sell lower that what is realised.
If price is lower, you win as you agreed to sell higher
than what is realised.
Futures contract
Agreement to buy or sell an asset for a certain price at a certain time.
Trades in an exchange. The maturity, size, and price are predetermined. Whereas forward contracts are traded
over-the-counter and are more customised.
Examples of futures contracts:
Arbitrage
Arbitrage is the possibility of a riskless profit. A trading strategy that:
- Does not cost anything to set up
- Will never have a negative cash flow
- Has the chance of earning a positive cash flow
We price these assets by assuming the derivatives derive their value on their underlying assets. So financial
derivative prices cannot have inconsistency (no arbitrage opportunity).
1. Gold: an arbitrage opportunity:
, N = contract
T = maturity
St = spot price at time 0
FtT = forward that you enter today at time little t, but
that will materialise at maturity capital T
Interest rate from time 0 to time 1
Assume you have no money to begin with. So at time 0, you borrow 1400$ at 5% for 1 year. You will buy gold
today at 1400$. Short 1 forward contract at 1500. If you borrow you will have to repay. If you brought gold, you
would want to sell it in the future. If you short the forward, you will have to deliver the asset.
At maturity, you will sell gold at 1500$. Repay loan of 1470$. Profit is money you pocketed in and money you
have to repay = 30$.
2. Gold
You can also borrow gold – the commodity. At time
0, you borrow gold and sell it at the spot market
getting 1400$.
When you keep money for one year, you invest it at
the IR getting 1470$. Buy the forward as it is cheap.
At maturity you take back 1470$, you buy gold for
1400$, and repay gold 1400$ making 70$.
For forward contracts, you don’t pay to enter, but is
has future obligation attached.
One of the formula to identify to be long or short: forward price of gold (ignores the gold lease rate) – per
annum compounding:
, 1. Oil example:
c = storage cost
At time 0, borrow 95$ at 5% p.a. with this money you can buy
oil at spot price because it is the cheap one. We want to short
the forward at price of 125$
At maturity, you sell oil at 125$ and repay your loan and storage
cost giving you a profit of 23.35$
Options
Options give you the right but not the obligation to fulfil the transaction. The rights do not come for free – you
pay them via premiums. Exercising the option (claiming it) when you benefit – if it does not benefit, you let it
mature/expire.
A call option gives the option holder the right to buy a certain asset (underlying) by a certain date (maturity,
expiration) for a certain price (the strike price)
A put option gives the option holder the right to sell a certain asset (underlying) by a certain date (maturity,
expiration) for a certain price (the strike price)
You can long or short a call or put option. Always think if you are the buyer – in terms of buyer and then switch
for the opposite.
E.g. a share of apple, you have a call option that tell you that you have the right to buy an apple share at 100$.
Tomorrow, you check the stock price and the share of apple is $500. You buy this because this generates you
400$ - this is an example where you exercise the call option. But what if it is $10 tomorrow, you will not
exercise the option and you will not lose money.
An instrument whose value depends on, or is derived from, the value of another underlying asset. E.g. futures,
forwards, swaps, options. Derivatives is intangible and expires (maturity). Derivatives play a key role in
transferring risks.
Financial transactions can have embedded derivatives (e.g. structured products). The underlying assets include
stocks, currencies, IR, commodities, weather – we can have derivatives whose underlying asset is interest rates.
Derivatives are traded in an exchange (dealing in standardised asset, so they’re telling you the maturity, strike
price, specific sizes of contract) or over-the-counter (more tailormade, you specify your needs of size, maturity
and price).
Derivatives are used for to hedge risks, to speculate (take a view on the future direction of the market and trade
on it to benefit), and arbitragers (in any state of the world, they will either break even or make money – it is a
no risk strategy, and trading two identical assets are priced differently -> profit).
Forward contracts
A forward contract is an agreement to buy or sell an asset at a certain future time (expiration, maturity) for a
certain, predetermined price (delivery price).
A spot contract is an agreement to buy or sell an asset today.
Long position: party has agreed to buy (ask/offer price). Short position: party has agreed to sell (bid price). Bid
ask spread is difference between the two prices – market maker profit for conducting the trade.
Example:
Possible outcomes:
- Higher exchange rate: you make money – you’ve
settled to a lower price than what is on the market.
- Lower exchange rate: you lose money – you’ve
agreed to pay a price that is too high than reality
, If future exchange rate is exactly the forward
contract price, then it will breakeven. If it is higher,
it will make a profit (difference between two prices)
and if it is lower, it will make a loss (difference
between two prices).
Shorting a forward contract: you are in it to sell and
not to buy.
If price is higher in the future, you lose money as
you’ve agreed to sell lower that what is realised.
If price is lower, you win as you agreed to sell higher
than what is realised.
Futures contract
Agreement to buy or sell an asset for a certain price at a certain time.
Trades in an exchange. The maturity, size, and price are predetermined. Whereas forward contracts are traded
over-the-counter and are more customised.
Examples of futures contracts:
Arbitrage
Arbitrage is the possibility of a riskless profit. A trading strategy that:
- Does not cost anything to set up
- Will never have a negative cash flow
- Has the chance of earning a positive cash flow
We price these assets by assuming the derivatives derive their value on their underlying assets. So financial
derivative prices cannot have inconsistency (no arbitrage opportunity).
1. Gold: an arbitrage opportunity:
, N = contract
T = maturity
St = spot price at time 0
FtT = forward that you enter today at time little t, but
that will materialise at maturity capital T
Interest rate from time 0 to time 1
Assume you have no money to begin with. So at time 0, you borrow 1400$ at 5% for 1 year. You will buy gold
today at 1400$. Short 1 forward contract at 1500. If you borrow you will have to repay. If you brought gold, you
would want to sell it in the future. If you short the forward, you will have to deliver the asset.
At maturity, you will sell gold at 1500$. Repay loan of 1470$. Profit is money you pocketed in and money you
have to repay = 30$.
2. Gold
You can also borrow gold – the commodity. At time
0, you borrow gold and sell it at the spot market
getting 1400$.
When you keep money for one year, you invest it at
the IR getting 1470$. Buy the forward as it is cheap.
At maturity you take back 1470$, you buy gold for
1400$, and repay gold 1400$ making 70$.
For forward contracts, you don’t pay to enter, but is
has future obligation attached.
One of the formula to identify to be long or short: forward price of gold (ignores the gold lease rate) – per
annum compounding:
, 1. Oil example:
c = storage cost
At time 0, borrow 95$ at 5% p.a. with this money you can buy
oil at spot price because it is the cheap one. We want to short
the forward at price of 125$
At maturity, you sell oil at 125$ and repay your loan and storage
cost giving you a profit of 23.35$
Options
Options give you the right but not the obligation to fulfil the transaction. The rights do not come for free – you
pay them via premiums. Exercising the option (claiming it) when you benefit – if it does not benefit, you let it
mature/expire.
A call option gives the option holder the right to buy a certain asset (underlying) by a certain date (maturity,
expiration) for a certain price (the strike price)
A put option gives the option holder the right to sell a certain asset (underlying) by a certain date (maturity,
expiration) for a certain price (the strike price)
You can long or short a call or put option. Always think if you are the buyer – in terms of buyer and then switch
for the opposite.
E.g. a share of apple, you have a call option that tell you that you have the right to buy an apple share at 100$.
Tomorrow, you check the stock price and the share of apple is $500. You buy this because this generates you
400$ - this is an example where you exercise the call option. But what if it is $10 tomorrow, you will not
exercise the option and you will not lose money.
