What do the Greeks measure?

Delta is sensitivity to the underlying, Gamma the change in Delta, Theta time decay per day, Vega sensitivity to a 1% volatility change and Rho to a 1% rate change.

Why is Theta negative?

Long options lose extrinsic value as expiry approaches, so their Theta (decay per calendar day) is negative. Short option positions have positive Theta.

Why is Gamma the same for calls and puts at the same strike?

Gamma measures the curvature of the option's value with respect to spot and is identical for a call and put at the same strike, expiry and volatility — only Delta and Rho differ.

What does a Delta of 0.64 mean in practice?

For every $1 move in the underlying, the option's price changes by about $0.64 in the same direction; it's also often read as an approximate probability of finishing in the money.

Why is Theta so much smaller for the put than the call here?

With a positive risk-free rate, discounting the strike works against the call's Theta and helps offset the put's, so at the same at-the-money strike the two Thetas usually differ noticeably.

How do I use Vega to judge an earnings trade?

Vega shows the price change per 1 percentage-point change in implied volatility; large Vega positions are more exposed to IV crush after an earnings announcement, independent of the stock's actual move.

Options

Option Greeks Calculator

Calculate option Greeks — Delta, Gamma, Theta (per day), Vega (per 1% vol) and Rho (per 1% rate) — from Black-Scholes inputs for calls and puts.

Option Greeks are sensitivities that measure how an option's price changes with the underlying price (delta, gamma), time (theta), volatility (vega) and rates (rho).

Delta

0.6368

Gamma: 0.01876
Theta / day: -0.0176
Vega / 1%: 0.3752
Rho / 1%: 0.5323
Option price: $10.45

Theta per calendar day; Vega per 1% vol; Rho per 1% rate. Long options have negative theta.

Worked example

Same 1-year at-the-money call: spot $100, strike $100, 5% rate, 20% volatility.

Delta: 0.637
Gamma: 0.0188 per $1 move
Theta: -$0.018 per calendar day
Vega: $0.375 per 1% vol change
Rho: $0.532 per 1% rate change

Per contract (×100 shares), this option loses about $1.76/day to time decay and gains about $37.50 in value for every 1 percentage-point rise in implied volatility.

How this is calculated

The Greeks are the derivatives of the Black-Scholes price:

Delta — sensitivity to a $1 move in the underlying.
Gamma — the rate of change of Delta.
Theta — decay per calendar day (we divide annual theta by 365).
Vega — price change per 1% change in volatility (÷100).
Rho — price change per 1% change in rates (÷100).

Long options always show negative Theta because their extrinsic value erodes as expiry approaches.

When to use this calculator

Use this when you hold or plan an options position and want to know how it behaves — how much it gains per $1 of underlying move (delta), how fast that changes (gamma), what each day of time decay costs (theta), and its sensitivity to volatility (vega).

It is most valuable before earnings or other events: vega tells you what a volatility crush would do to the position, often a larger effect than the price move itself.

Position management is the other main use. Traders who target a portfolio delta, or who want to know when theta decay accelerates into expiry week, can read those figures directly instead of estimating them.

Common mistakes

Reading Theta as a daily dollar cost without multiplying by the contract multiplier (typically 100 shares per option contract).
Comparing raw Vega/Rho across options with very different prices instead of normalising per $1 of premium.
Assuming Delta stays constant as the underlying moves — it changes continuously, which Gamma measures.

Frequently asked questions

What do the Greeks measure?: Delta is sensitivity to the underlying, Gamma the change in Delta, Theta time decay per day, Vega sensitivity to a 1% volatility change and Rho to a 1% rate change.
Why is Theta negative?: Long options lose extrinsic value as expiry approaches, so their Theta (decay per calendar day) is negative. Short option positions have positive Theta.
Why is Gamma the same for calls and puts at the same strike?: Gamma measures the curvature of the option's value with respect to spot and is identical for a call and put at the same strike, expiry and volatility — only Delta and Rho differ.
What does a Delta of 0.64 mean in practice?: For every $1 move in the underlying, the option's price changes by about $0.64 in the same direction; it's also often read as an approximate probability of finishing in the money.
Why is Theta so much smaller for the put than the call here?: With a positive risk-free rate, discounting the strike works against the call's Theta and helps offset the put's, so at the same at-the-money strike the two Thetas usually differ noticeably.
How do I use Vega to judge an earnings trade?: Vega shows the price change per 1 percentage-point change in implied volatility; large Vega positions are more exposed to IV crush after an earnings announcement, independent of the stock's actual move.