# 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. Part of [Glossary Index](/blog/glossary-index) · Previous: [Backtesting & Validation](/blog/glossary-index/glossary-backtesting-and-validation) · Next: [Trading Systems & Market Connectivity](/blog/glossary-index/glossary-trading-systems-market-conn)