Explore a mathematical model of European calls and puts.
MODEL / 01
Black–Scholes–Merton estimates a theoretical option value from six
inputs. Change an assumption and observe how the value and sensitivities change. This
calculator uses hypothetical inputs; it does not use an option chain or recommend a trade.
Start with the assumptions.
Enter six inputs and calculate theoretical call and put values.
THEORETICAL VALUE / PER OPTION UNIT
European call
European put
How sensitive is the value?
These are model derivatives at the chosen inputs, not estimates of future profit.
Measure
Call
Put
Delta: value change per $1 underlying move. Gamma: delta change per $1. Vega:
value change per 1 percentage-point volatility move. Theta: value change per
calendar day. Rho: value change per 1 percentage-point rate move. These are local
sensitivities, not exact outcomes for large changes.
One input at a time.
Hypothetical spot-price scenarios; strike, time, rates, dividend yield, and
volatility stay fixed. Each row is recalculated from the model.
Spot change
Spot
Call value
Put value
MODEL NOTES
What the calculation assumes.
The model prices European options, exercisable only at expiry. It assumes constant
volatility and risk-free rate, a continuous dividend yield, and frictionless trading.
Actual options have changing volatility, bid/ask spreads, and other market effects. A
theoretical price is not a tradable quote or a historical backtest.
The displayed prices use
call = S·e−qT·N(d₁) − K·e−rT·N(d₂) and put–call
parity call − put = S·e−qT − K·e−rT. The implementation has tests for a standard numerical benchmark, parity, Greeks, and
limiting behavior. Read the
original paper ↗ or the
source code ↗.
To study historical options trading, Orion would need point-in-time contract chains,
executable prices, and an explicit entry, exit, and cost model. That work is separate
from this calculator. Return to strategy backtesting ↗