Derivatives: Futures, Options & Greeks
Szymon Kopyciński · 23 September 2026
1. Futures and forwards
Forward
A contract agreeing today to buy or sell something at a specified price on a future date.
Forwards are traded OTC.
Futures contract
A standardised contract to buy or sell an underlying asset at a specified price on a future date.
Futures are exchange-traded, centrally cleared and marked to market daily.
Expiry
The date on which a derivative contract expires.
Contract size
The amount of underlying exposure represented by one derivative contract.
Front month
The futures contract with the nearest expiry.
It is usually, but not always, the most liquid contract.
Roll
Closing a position in an expiring futures contract and opening an equivalent position in a later expiry.
Contango
A futures curve where later-dated contracts trade at higher prices than nearer-dated contracts.
Backwardation
A futures curve where later-dated contracts trade at lower prices than nearer-dated contracts.
Mark-to-market
For futures, gains and losses are settled daily through variation margin paid to or received from the clearing house.
2. Options
Option
A derivative giving its holder the right, but not the obligation, to buy or sell an underlying asset at a specified price.
Call option
An option giving the holder the right to buy the underlying at the strike price.
Put option
An option giving the holder the right to sell the underlying at the strike price.
Strike
The price at which the underlying may be bought or sold under the option contract.
Premium
The price paid to buy an option.
Expiration / Expiry
The date on which the option ceases to exist.
Exercise
Using the right granted by an option.
European option
An option that can only be exercised at expiry.
The name does not refer to where the option trades.
American option
An option that can be exercised at any time up to and including expiry.
As with European options, the name does not refer to geography.
ITM / In-the-money
An option with positive intrinsic value.
For a call: $S > K$. For a put: $S < K$.
Here $S$ is the underlying price and $K$ is the strike.
ATM / At-the-money
An option whose strike is approximately equal to the current underlying price.
OTM / Out-of-the-money
An option with no intrinsic value because its strike is on the unfavourable side of the underlying price.
For a call: $S < K$. For a put: $S > K$.
Intrinsic value
The value an option would have if exercised immediately.
For a call:
$$ \max(S - K, 0) $$
For a put:
$$ \max(K - S, 0) $$
Time value
The portion of an option's price above its intrinsic value.
It reflects the chance that market movements before expiry make the option more valuable.
Implied volatility / IV
The volatility that makes an option-pricing model match an option's observed market price.
Traders frequently quote options in terms of implied volatility rather than price.
3. The Greeks
Delta
The sensitivity of an option's value to a small change in the underlying price.
$$ \Delta = \frac{\partial V}{\partial S} $$
A call has delta between 0 and 1. A put has delta between −1 and 0.
Gamma
The sensitivity of delta to changes in the underlying price.
$$ \Gamma = \frac{\partial^2 V}{\partial S^2} $$
High gamma means an option's directional exposure changes quickly as the underlying moves.
Vega
The sensitivity of an option's value to changes in implied volatility.
Despite the name, vega is not a Greek letter.
Theta
The sensitivity of an option's value to the passage of time.
Long options usually have negative theta because their time value decays as expiry approaches.
Rho
The sensitivity of an option's value to interest rates.
Volatility smile
A pattern where implied volatility varies by strike rather than remaining constant, rising for strikes further from the money.
Volatility skew
An asymmetric relationship between implied volatility and strike.
Equity index options typically show higher implied volatility for downside strikes.
Volatility surface
Implied volatility across both strike and time to expiry.
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