Options Greeks Explained: Delta, Gamma, Theta, Vega, Rho

By Rohan Fernandes, Founder · Updated 2026-08-21 · Educational reference, not investment advice

What does each first-order greek measure?

• Delta (Δ) is the option price change per $1 move in the stock: calls run 0 to +1, puts 0 to -1. It doubles as a rough proxy for the probability of finishing in the money and as the position's stock-equivalent exposure: a 0.30-delta call moves like 30 shares.
• Gamma (Γ) is the change in delta per $1 move: the curvature. It peaks at the money and accelerates into expiration. Long options own gamma (exposure grows in the favorable direction); short options owe it.
• Theta (Θ) is the option price change per day of time passing, quoted per calendar day. Premium sellers collect it; premium buyers pay it. For credit structures the practical harvest window is roughly 21-45 days to expiration, where decay is meaningful and gamma still shallow.
• Vega (ν) is the price change per one-point move in implied volatility. Debit structures and straddles are long vega; credit spreads and condors are short vega, which is why they are screened for rich volatility at entry.
• Rho (ρ) is the sensitivity to the risk-free rate. Negligible for short-dated trades; material for LEAPS, where a rate change compounds over years, and one reason careful pricing uses a per-expiry yield curve rather than one constant rate.

What are charm, vanna, and vomma?

Second-order greeks: charm is delta's drift as time passes (a 0.30-delta strike does not stay 0.30 overnight), vanna is delta's response to volatility changes, and vomma is vega's response to volatility changes. They stay academic in quiet tape and become the story during volatility shocks and large dealer-hedging flows, when positions change character without the stock moving at all.

Why read a whole portfolio in greeks?

Positions that look unrelated share exposures. Ten individually reasonable credit spreads can sum to one large short-vega, short-gamma position that a single volatility event hits all at once. Aggregating net delta, gamma, theta, and vega across the book, beta-weighted to a common index, is what reveals that concentration while it is still cheap to fix, and portfolio-level caps on those aggregates are the standing defense.

Frequently asked questions

Which greeks change fastest as expiration approaches?

Gamma and theta both concentrate near the strike in the final weeks: gamma makes delta swing harder for the same price move, and theta accelerates time decay. Vega drains away, since there is less time for a volatility change to matter. This migration is why the same structure behaves so differently at 40 days and at 5 days.

Do greeks describe a contract or a position?

Both. Each contract carries its own greeks, and a position's greeks are the sum across legs, signed by direction. Summing across an account, with each name's delta weighted by its relationship to a benchmark, produces the portfolio-level view used for book-level risk reads.

Why are greeks called estimates rather than facts?

Each greek is a model derivative evaluated at current inputs, so it describes sensitivity to small moves under the model's assumptions. Large gaps, volatility regime changes, and dividend or rate surprises move an option in ways the point-in-time greeks do not fully capture.