Playground
Options Greeks Calculator (Black-Scholes)
Black-Scholes options pricer + live Greeks visualizer. Drag spot, strike, vol, DTE, rate, dividend yield; see delta/gamma/theta/vega/rho. Free to use.
Runs in your browser. Nothing you enter is uploaded, and no account or API key is needed.
Inputs
Tap the value to type an exact price.
Calendar days; T = days ÷ 365.
Delta
+0.535
Long call: gains when spot rises. A $1 rise in spot changes the option value by $0.535 per share. ATM, balanced spot vs. vol risk.
Price $3.04. Vega $0.114/1%σ. Theta −$0.054/day. Call, strike 100, 30 days
Greeks
Price
$3.0418
CALL Black-Scholes
Delta
0.535
∂Price / ∂Spot
Gamma
0.0554
∂Delta / ∂Spot
Theta (per day)
−$0.0537
∂Price / ∂T
Vega (per 1%)
$0.1139
∂Price / ∂σ
Rho (per 1%)
$0.0415
∂Price / ∂r
Value today (solid) vs payoff at expiry (dashed)
Spot ±40%; vertical line = current spotBreakdown
Intrinsic
$0.0000
Extrinsic (time)
$3.0418
Put price (parity)
$2.6727
same inputs, flipped type
Moneyness
1.000
S / K
Model
Generalized Black-Scholes with continuous dividend yield q:
d1 = [ln(S/K) + (r − q + σ²/2)·T] / (σ·√T) d2 = d1 − σ·√T call = S·e^(−qT)·Φ(d1) − K·e^(−rT)·Φ(d2) put = K·e^(−rT)·Φ(−d2) − S·e^(−qT)·Φ(−d1)
Reported Greeks are per-day for theta, per 1% vol point for vega, per 1% rate for rho.
How to use it
- Choose call or put, then set spot, strike, implied volatility, days to expiry, risk-free rate and dividend yield. Tap any value to type an exact number.
- Read delta in the result, with the option's Black-Scholes price, vega and theta under it.
- Check the Greeks row: gamma, theta per calendar day, vega per volatility point and rho per 1% rate move.
- Use the chart to compare today's option value with the payoff at expiry across spot ±40%.
- Read the breakdown for intrinsic and time value and the opposite option's price at the same inputs.
Questions people ask
Which pricing model does the tool use?
Generalized Black-Scholes for European options with a continuous dividend yield (Merton's extension). There is no American-exercise model, so the price does not include any early-exercise premium.
What are the Greeks measuring?
Delta is sensitivity of option price to a $1 underlying move. Gamma is the rate of change of Delta. Theta is daily time-decay (premium lost per day, holding all else constant). Vega is sensitivity to a 1-percentage-point implied volatility change. Rho is sensitivity to a 1-percentage-point interest-rate change.
Why does Vega look high near at-the-money?
Vega is largest near the money and falls toward zero as the option moves deep in or out of the money, because the value of a near-the-money option depends most on how far the underlying might travel. Move the strike away from spot and watch vega fall; the page shows vega for the selected strike, not a sweep across strikes.
Does the tool include American early-exercise premium?
No. Prices are European. For calls on a stock with no dividend, early exercise is never optimal, so the American and European prices match. For puts, and for calls on dividend payers, an American option can be worth more than the price shown.
What if I want to price exotics?
The tool handles vanilla European calls and puts only. Barriers, Asians, lookbacks and digitals need Monte Carlo or dedicated closed-form models; open-source libraries such as QuantLib implement most of them.
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Articles
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Options Greeks for LLM-driven trading: delta, gamma, theta, vega, rho — what each costs, three rules, plus a prompt template for multi-leg positions.
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Use it from code
The same calculation as a JavaScript module you can import. It runs where you import it, with no request, key or rate limit.
import { compute } from "https://aifinhub.io/engines/options-greeks-explorer.js";