Option convexity
Definition · Level 5 · Greeks & volatility
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Curvature of option P&L versus the underlying: beyond the linear delta P&L, the holder gains about ½ × gamma × move² whichever way the stock goes.
Example
Position gamma +100, stock moves $4 → about +$800 extra.
Where Tradecraft teaches it
Level 5 · Greeks & volatility, in the lesson “Gamma & theta: convexity and its rent”: Why delta moves, why options decay, and why you can’t have one without the other.
Related terms
- Breakeven moveThe daily underlying move at which a delta-hedged option’s gamma P&L just covers its time decay: √(2 × |daily theta $| ÷ position gamma).
- GammaRate of change of delta per $1 move in the underlying; peaks near the money, and near-the-money values rise as expiry approaches.
- 25-delta optionThe OTM call or put whose delta is ±0.25 — the standard reference strike for quoting skew; very roughly a 1-in-4 chance of finishing in the money.
- Black–ScholesEuropean option-pricing model using spot, strike, time, rates, dividends and volatility; assumes lognormal prices, constant vol, no jumps and…
- Butterfly (vol quote)Smile-curvature quote: average of the 25Δ call and 25Δ put IVs minus ATM IV — how rich the wings are relative to the money.
- CharmSecond-order Greek: change in delta as time passes (“delta decay”).