Options & Derivatives
The Greeks: Decoding How Options Prices Move
Delta, Gamma, Theta, Vega, and Rho explain exactly how an option's price responds to changes in the underlying price, time, volatility, and interest rates.
Key rules
- Delta: option price change per $1 move — also approximates probability of expiring ITM
- Theta: daily time decay — works against buyers and in favour of sellers (accelerates near expiration)
- Vega: sensitivity to Implied Volatility — long options benefit from rising IV; short options suffer
- Gamma: rate of Delta change — high near expiration for ATM options; creates rapid gains/losses for both sides
- High IV = expensive options (good for sellers); Low IV = cheap options (good for buyers)
The 'Greeks' are mathematical measures of an option's sensitivity to various factors. Understanding them is not optional if you trade options — they are the language in which option price behaviour is described.
**Delta (Δ) — Price Sensitivity** Delta measures how much the option's price changes for a $1 move in the underlying. A Delta of 0.50 means the option gains $0.50 for every $1 the stock rises. ATM options have ~0.50 Delta; deep ITM options approach 1.0; far OTM options approach 0. Delta also approximates the probability the option expires ITM (a 0.30 Delta option has ~30% chance of expiring ITM).
**Gamma (Γ) — Delta Sensitivity** Gamma measures how much Delta changes for a $1 move in the underlying. High Gamma means Delta can change rapidly — near expiration, ATM options have very high Gamma, meaning a small stock move can dramatically change the option's Delta (and value). Gamma accelerates gains for buyers and losses for sellers near expiration.
**Theta (Θ) — Time Decay** Theta is the daily rate at which the option loses time value, all else being equal. A Theta of -0.05 means the option loses $5/day (per contract of 100 shares). Time decay accelerates as expiration approaches — ATM options lose the most time value in the final 30 days. Buyers fight Theta; sellers collect it.
**Vega (ν) — Volatility Sensitivity** Vega measures the change in option price for a 1% change in Implied Volatility (IV). Long options gain from rising IV (Vega positive); short options lose from rising IV. This is why selling options before earnings (when IV is elevated) then watching IV collapse post-announcement ("IV crush") is a common income strategy.
**Rho (ρ) — Interest Rate Sensitivity** Rho measures sensitivity to interest rate changes. For most retail option traders, Rho is the least important Greek. It matters more for long-dated (LEAPS) options and during periods of significant rate changes.
**Practical Greeks Summary** - Want the option to move with the stock? Focus on Delta. - Worried about time running out? Monitor Theta — longer expiration = less Theta damage. - Expecting volatility to spike? Own high Vega options (buy them before the catalyst). - Selling premium? Collect Theta and hope Vega stays low.