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Institutional · Derivatives Pricing
Black-Scholes-Merton Options Pricing Engine
Live theoretical call and put pricing with the full Greek profile, the same closed-form model institutional desks use to hedge delta risk.
Reading This Tool
How To Use This Calculator
Enter the underlying price, strike price, time to expiration, risk-free rate and implied volatility, the same five inputs behind every options pricing terminal on a trading desk.
The table gives the full Greek profile for both the call and the put; the chart shows how the call's value bleeds away as expiration approaches, holding everything else fixed. Try moving only the volatility slider and compare how much more that shifts the price than an equivalent move in the underlying, that gap is exactly what vega measures.
Your Inputs
Theoretical Pricing
-Call Price
$0.00
Put Price
$0.00
d1
0.00
d2
0.00
| Greek | Call | Put | What It Measures |
|---|---|---|---|
| Delta | 0.00 | 0.00 | Price change per $1 move in the underlying |
| Gamma | 0.0000 | 0.0000 | Rate of change of delta itself |
| Vega | 0.00 | 0.00 | Price change per 1pt move in volatility |
| Theta (per day) | 0.00 | 0.00 | Value lost per day as expiration approaches |
| Rho | 0.00 | 0.00 | Price change per 1pt move in interest rates |
Call Premium Decay As Expiration Approaches
Black-Scholes-Merton assumes constant volatility, continuous trading, no transaction costs, and log-normally distributed returns, assumptions real markets violate, especially around earnings events and tail risk. This is the standard teaching and first-approximation model, not a production pricing system.