Gamma

In plain words

Gamma is delta's "acceleration" — it shows how quickly an options position's risk profile changes as the price moves.

In more detail

Gamma measures the change in delta for a move in the underlying and is therefore the second derivative of the option price. It is largest at the money and close to expiry, where a small move decides between exercise and expiry. For the writer gamma is the actual source of danger: a negative gamma position requires buying as prices rise and selling as they fall, trading against oneself, and the cost of those adjustments grows with the square of the move. The buyer holds mirror-image positive gamma and earns from movement while paying time value continuously. The economic core of every option position is precisely that exchange — gamma against theta.

Formula

Γ = ∂²V/∂S² = ∂Δ/∂S

The second derivative of the option price with respect to price — equivalently, the first derivative of delta with respect to price.

Example

1. An at-the-money option has a gamma of 0.08. A two point move in the underlying changes delta by 0.16 — the writer must adjust 16 percent of the position. 2. On expiry day that same gamma rises to 0.61. The same two point move now requires a 122 percent adjustment; hedging costs more than the premium collected.

What it means for traders

Central to understanding gamma exposure and dealer hedging dynamics, which can amplify or dampen short-term market moves.

Common pitfalls

Writers with negative gamma (option sellers) face disproportionate loss risk during sharp price moves.

Related terms

At-the-Money (ATM) · Color · Delta (Δ) · Delta Hedge · Gamma Exposure (GEX) · Gamma Hedging · Gamma Neutral · Gamma Scalping · Speed · Vanna · Zomma