Gamma

简要解答

Gamma measures how quickly delta changes as the stock price moves. If a call has a delta of 0.50 and a gamma of 0.05, a one-dollar rise in the stock lifts its delta to about 0.55. Delta describes the option's current sensitivity; gamma describes how fast that sensitivity shifts.

Gamma is largest for at-the-money options and grows as expiration approaches. That combination is why an at-the-money option in its final days can swing sharply in value on ordinary stock moves.

Long calls and long puts both carry positive gamma from the holder's side. As with the other greeks on Options Band, the displayed gamma comes from Cboe's delayed feed.

深入了解

Take a stock at $100 and an at-the-money $100 call with a delta of 0.50 and a gamma of 0.05. A rise to $101 earns roughly $0.50 and lifts the delta to about 0.55, so the next dollar — from $101 to $102 — earns about $0.55. Each step up makes the option more sensitive, and each step down makes it less sensitive. The curvature works in the holder's favor in both directions: gains accelerate while losses decelerate.

Moneyness matters. A far out-of-the-money $130 call on the same stock might carry a gamma of just 0.01: its delta barely moves until the stock gets much closer to the strike.

Time matters more. With six months to expiration, an at-the-money option's gamma is spread thin, because one dollar of stock movement barely changes the odds of finishing in the money. With three days left, the same strike's gamma is several times larger — the option is close to flipping between worthless and stock-like, and its delta lurches with every move.

Curvature is not free. The positions that hold high gamma also carry heavy time decay, measured by theta: the stock has to actually move for the curvature to be worth its daily rent. The size of the move the options market itself anticipates is summarized in the expected move.

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Gamma is the second partial derivative of option value with respect to the underlying price — equivalently, the first derivative of delta.

Γ = ∂²V/∂S² = ∂Δ/∂S

By put-call parity, a European call and put with the same strike and expiration have identical gamma. Gamma peaks near the at-the-money strike, and as expiration approaches it grows without bound for the at-the-money option while collapsing toward zero everywhere else — which is why short-dated chains show gamma concentrated in a narrow band of strikes.

A frequent misreading treats high gamma as inherently favorable. Gamma is curvature, not edge: a position holding it pays through theta, and the outcome depends on how much the stock actually moves relative to that cost. Gamma is also a local measure — a delta adjusted using gamma is accurate only for small changes, and large gaps invoke higher-order terms the chain does not display. Because Options Band's figures come from Cboe's delayed feed, gamma on fast-moving days will lag the live surface.