OptionMetricGreeks workbench
Black–Scholes · European options

Price the contract.
Read the risk.

A European valuation that updates as you type, with every first-order sensitivity beside it. Change one number and watch the greeks move.

calllong 1 contractOTM

Theoretical value

$1.45per share

1.45%of spot

Total premium
$144.69
Intrinsic
$0.00
Time value
$1.45
Breakeven
$106.45

Risk sensitivity

ΔDelta
+0.297
per $1Direction
ΓGamma
+0.043
Δ per $1Convexity
ΘTheta
−0.049
per dayDecay
νVega
+0.099
per vol ptVolatility
ρRho
+0.023
per rate ptRates

Payoff at expiry

long call, held to expiration

Breakeven$106.45
Max profitUnlimited
Max loss−$144.69

Across the spot

How each metric bends as the underlying moves, expiry held fixed

Back out volatility

Enter the price the market is paying and solve for implied volatility.

Market price

Implied volatility

Waiting on a market price.

Model vol28.00%

Scenario grid

Position P&L for simultaneous spot and implied-volatility shocks, time held constant

Gain Loss
Vol / Spot−10%−5%Flat spot+5%+10%
−10 vol−$144.45−$138.78−$90.78+$86.18+$434.74
−5 vol−$142.32−$124.31−$47.88+$146.01+$477.66
Flat vol−$135.75−$100.88+$0.00+$205.84+$526.37
+5 vol−$123.35−$70.27+$50.84+$265.67+$578.57
+10 vol−$105.03−$34.27+$103.56+$325.49+$632.99

Reading the greeks

ΔDelta

Price change for a $1 move in the underlying, and the hedge ratio: 0.50 means 50 shares per contract.

ΓGamma

How fast delta itself changes. Peaks at-the-money and near expiry, where exposure flips quickest.

ΘTheta

Value surrendered as one day passes with spot and volatility unchanged. Negative for long options.

νVega

Price change for a one point shift in implied volatility. Long options gain when vol rises.

ρRho

Price change for a one point shift in the risk-free rate. Small over short expiries.