Black-Scholes Options Pricer
Call price
2.493376
Put price
2.083261
Delta Call
0.539964
Delta Put
-0.460036
Gamma
0.069228
Vega
0.113799
Theta Call
-0.044988
Theta Put
-0.031346
Rho Call
0.042331
Rho Put
-0.039523
FAQ
Black-Scholes model
What is the Black-Scholes model?
A mathematical model for pricing European options. Assumes geometric Brownian motion of the underlying, constant volatility and risk-free rate, no arbitrage. Nobel Prize 1997.
What are the "Greeks"?
Sensitivities of the option price to external factors: Delta (spot price), Gamma (delta change), Theta (time decay), Vega (vol), Rho (rate). Crucial for risk management.
What inputs does the Black-Scholes calculation need?
The spot price of the underlying, the strike, the days left to expiry, the risk free rate, the annual volatility and the dividend yield, the last three given as percentages.
Which greeks are worked out?
Delta for the call and the put, Gamma, Vega, Theta for both and Rho for both, that is, how the price responds to spot, volatility, the passing of time and interest rates.
Does the model hold for American options?
Black-Scholes prices European options, the ones exercisable only at expiry, and assumes volatility and rates stay constant. On American options the result stays an approximation.