US Options Greeks Calculator
Input underlying price, strike, time, volatility and rate to get theoretical value and Greeks.
Calculator Inputs
Valuation & Greeks Result Chart
SPY · $500.00Continuous Black-Scholes Call & Put theoretical curves across underlying spot prices. Hover across the curve to inspect instantaneous premiums and Deltas.
Primary Results & Quantitative Sensitivities
CALL OPTION (ATM)
Long Bullish ExposurePUT OPTION (ATM)
Short / Hedge Exposuretable_chart Strike Sensitivity Matrix (SPY Expiry Ladder)
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Understanding the Black-Scholes Options Greeks
The "Greeks" are mathematical first and second partial derivatives of the Black-Scholes-Merton options pricing model that quantify how contract premiums fluctuate in response to underlying price shifts, volatility swings, interest rates, and the continuous erosion of time.
Delta (Δ) — Price Sensitivity
Calls: 0 to +1 | Puts: -1 to 0Measures the dollar change in theoretical option premium per $1.00 move in the underlying asset. A Call Delta of +0.528 indicates the contract gains $0.528 per share if the underlying advances $1.00. Delta also serves as an accurate proxy for the probability of expiring in-the-money (ITM).
Gamma (Γ) — Delta Acceleration
Always Positive for LongsThe second derivative with respect to underlying spot: measures the rate at which Delta changes for each $1 move. Gamma peaks sharply for at-the-money (ATM) options approaching expiration, driving extreme non-linear payoff swings (known as Gamma Risk).
Theta (Θ) — Daily Time Decay
Typically Negative for BuyersQuantifies the inevitable daily erosion of extrinsic time value. For long weekly options, Theta decays non-linearly, accelerating dramatically over the final 7 to 14 days before expiration.
Vega (ν) — Volatility Sensitivity
Premium per 1.0% IV ChangeMeasures contract price sensitivity to a 100-basis-point (1.0 percentage point) fluctuation in implied volatility (IV). High Vega positions suffer rapid valuation loss during post-earnings "volatility crush."
Rho (ρ) — Interest Rate Sensitivity
Calls (+) | Puts (-)Sensitivity of contract price to a 1.0% (100 bps) shift in the risk-free US Treasury borrowing rate. Generally more impactful on long-dated leaps (LEAPS) than short-term weeklies.
Mathematical Model
Black-Scholes-Merton continuous closed-form equation with dividend yield adjustment:
Options Greeks FAQ
Why is Gamma highest for ATM options near expiry? expand_more
Because an at-the-money option on the edge of expiration is hyper-sensitive to whether it settles 1 cent in or out of the money. A tiny move flips the probability of expiration from 0% to 100%, causing Delta to swing violently.
How does IV crush impact Vega after earnings? expand_more
Before corporate earnings, implied volatility surges due to unknown binary outcomes. Once announced, uncertainty evaporates and IV drops instantly. With a Vega of $0.27, a 20% drop in IV strips $5.40/share from contract extrinsic value regardless of underlying movement.
Can Delta ever exceed 1.0 or fall below -1.0? expand_more
No. In single standard American or European equity contracts, Delta ranges strictly between 0.0 and +1.0 for Calls, and between 0.0 and -1.0 for Puts, corresponding directly to the fractional share equivalence per contract.
How do dividends affect Call and Put pricing? expand_more
When a stock goes ex-dividend, its share price drops by roughly the dividend amount. Therefore, high dividend yields reduce Call values (negative Call sensitivity) while increasing Put values (positive Put sensitivity).
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