Options are non-linear instruments: their value does not move in a simple straight line with the underlying price. The Greeks are the set of risk measures that describe how an option's value changes as market inputs change — they are the language of options risk management.
Delta: directional exposure
Delta measures how much an option's value changes for a one-unit move in the underlying price. A call option with delta 0.6 gains approximately 60 pence in value for every £1 rise in the underlying stock. Delta ranges from 0 (deep out of the money) to 1 (deep in the money) for calls, and 0 to -1 for puts.
Delta-hedging — holding a position in the underlying that exactly offsets the option's delta — creates a theoretically risk-neutral position. But because delta changes as the underlying moves, hedges must be continuously rebalanced. This continuous rebalancing is the primary activity of options market makers.
Gamma: the curvature
Gamma measures how quickly delta changes as the underlying moves. A long gamma position gains delta as the underlying rises (and loses delta as it falls) — benefiting from large moves in either direction. A short gamma position is the mirror: it loses money from large moves and gains from stability.
Structured product desks that sell autocalls to clients are naturally short gamma. Managing this exposure — buying gamma through listed options to partially offset the short — is one of the largest and most continuous activities in equity derivatives.
Vega and Theta
Vega measures sensitivity to implied volatility: when volatility rises, options become more valuable (the range of possible outcomes widens). Theta measures time decay: options lose value every day as expiry approaches, all else equal. Option sellers earn theta; buyers pay it.
Managing a book of Greeks