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Option Greeks describe model-based sensitivities of option value to inputs such as underlying price, volatility and time.

About 2 min to read · Take extra time for practice · AI-assisted learning notes · Expanded October 17, 2026

First, the key terms.

Delta: First-order sensitivity to the underlying price.
Gamma: Sensitivity of delta to the underlying price.
Vega: Sensitivity to a specified volatility change convention.

The idea, explained

Delta measures first-order sensitivity to the underlying price; gamma describes how delta changes. Vega measures sensitivity to a volatility input, and theta describes a time sensitivity under a specified convention. These are local estimates that change with market conditions and model assumptions. A hedge based on delta can become inaccurate as the underlying moves. Liquidity, exercise features and transaction costs complicate theoretical hedging.

STEP 1

Hold other inputs fixed

A Greek isolates a small change under assumptions. In real markets, price, volatility and time change together. Check whether a quoted value is per unit or per contract and which volatility convention applies.

STEP 2

Update the hedge

A delta hedge is local. Gamma means the required offset changes as the underlying moves. Transaction costs, gaps and model error prevent theoretical continuous hedging from being a simple real-world guarantee.

Follow a worked example.

An illustrative call has delta 0.60. A $1 rise in the underlying suggests about a $0.60 increase per option unit for a sufficiently small move with other inputs fixed. The estimate is not exact and says nothing by itself about a large price gap.

Walk it through, one step at a time

A fictional option has delta 0.4 per underlying unit. A small $2 rise suggests approximately $0.80 option-value change with other inputs fixed.
If the contract covers 100 units, the approximate contract change is $80.
A large move can make this estimate inaccurate because delta itself changes and other inputs may move.

Where people get stuck

Delta is not a fixed percentage guarantee, and a sensitivity estimate is not a complete loss limit.

Now try it yourself.

Pause before opening each answer. Explain your reasoning in your own words.

1. Check the core idea

Why can a delta-neutral position become directional after the market moves?

Reveal the answer & reasoning

Gamma changes delta as the underlying price changes, and other inputs may move too. Neutrality is local rather than permanent.

2. Apply what you learned

Does delta 0.4 mean the option will gain 40 percent?