Options Greeks

What It Measures

Delta measures how much an option's price is expected to change for every $1 move in the underlying asset. A delta of 0.50 means the option's price should rise (or fall) by $0.50 for each $1 move in the stock.

How It Works

• → Call options always have positive delta (0 to +1). When the stock rises, calls gain value.
• → Put options always have negative delta (-1 to 0). When the stock rises, puts lose value.
• → Deep in-the-money options have delta near ±1 and move almost dollar-for-dollar with the stock.
• → At-the-money options typically have delta near ±0.50. Far out-of-the-money options approach 0.
• → Delta also approximates the probability that the option expires in the money.

Practical Use

Traders use delta to size positions and build delta-neutral hedges. Summing the deltas of all positions gives you your overall directional exposure. A portfolio with net zero delta has no directional bias from small price moves.

What It Measures

Gamma measures how much delta changes for each $1 move in the underlying. If delta is the speed of an option's price change, gamma is its acceleration. A gamma of 0.05 means delta will increase by 0.05 for every $1 rise in the stock.

How It Works

• → Gamma is highest for at-the-money options and rises sharply as expiration approaches.
• → Long options (calls and puts) have positive gamma. Short options have negative gamma.
• → High gamma means delta is unstable — a small move in the underlying causes a large delta shift.
• → Gamma risk is the danger that your delta changes unexpectedly as the underlying moves, making hedges quickly go stale.

Practical Use

Market makers and institutional traders track gamma to understand how often they need to re-hedge their delta. Traders long gamma (long options) benefit when the underlying makes large moves. Traders short gamma (premium sellers) are hurt by large moves. Gamma spikes in the final week before expiration — making short options especially risky near expiry.

What It Measures

Theta measures how much an option's price declines each day due to the passage of time, all else being equal. A theta of -0.05 means the option loses $0.05 of value per day. This erosion is called time decay.

How It Works

• → Long options always have negative theta — you lose value every day you hold them.
• → Short options have positive theta — time decay works in your favor as the seller.
• → Time decay is non-linear — it accelerates dramatically in the final 30 days before expiration.
• → ATM options have the highest theta. Deep ITM and deep OTM options have lower theta.
• → Higher implied volatility leads to higher theta, since options with more premium have more to decay.

Practical Use

Premium sellers (short straddles, iron condors, covered calls) deliberately collect theta — the position earns money each day the underlying stays flat. Options buyers fight theta and need a significant move to overcome it. The key tradeoff: theta and gamma are inversely related. Positions with high positive theta (premium sellers) are exposed to large gamma risk if the underlying moves sharply.

What It Measures

Vega measures how much an option's price changes for each 1% change in implied volatility (IV). A vega of 0.10 means the option gains or loses $0.10 for every 1-point move in IV. Unlike the other Greeks, vega is not an actual Greek letter — it's a term unique to options trading.

How It Works

• → Long options have positive vega. Rising IV increases the value of both calls and puts.
• → Short options have negative vega. Rising IV hurts short positions; falling IV helps them.
• → Vega is highest for ATM options and for options with more time to expiration.
• → After earnings or major events, IV often collapses — a phenomenon called the volatility crush — which can devastate long option positions even if the stock moves in the right direction.

Practical Use

Traders use vega to assess whether options are cheap or expensive relative to historical norms. Buying options when IV is historically low (low vega risk) and selling when IV is historically high (positive theta, negative vega) is a core principles of volatility trading. Tools like the IV Rank (IVR) and IV Percentile contextualize current IV relative to its historical range.

What It Measures

Rho measures how much an option's price changes for each 1% change in the risk-free interest rate. A rho of 0.05 means the option gains $0.05 for every 1-percentage-point rise in rates. Rho is the least commonly referenced Greek for short-dated options but becomes important for LEAPS.

How It Works

• → Call options have positive rho: rising interest rates increase call values (cost of carry makes owning stock more expensive, making calls relatively more attractive).
• → Put options have negative rho: rising interest rates decrease put values.
• → Rho grows with time to expiration — it is much larger for LEAPS than for weekly options.
• → Options with high underlying prices have higher rho sensitivity than lower-priced underlyings.
• → Near expiration, rho approaches zero regardless of other factors.

Practical Use

For most short-term equity option traders, rho has a minor effect and is often ignored. It becomes more relevant when trading deep-in-the-money options, LEAPS, or during periods of rapid interest rate change. During significant Fed rate cycles, traders managing multi-leg positions in longer-dated options may track rho exposure across their portfolio.