Options Calculator
American and European Options Pricer using Binomial Tree and Black-Scholes Models
Input Parameters
Current market price of the underlying asset
Price at which the option can be exercised
Time until option expiration
Annual volatility of the underlying asset
Annual risk-free interest rate
Greeks
delta0.0000
Change in option price per $1 change in underlying
gamma0.0000
Rate of change in delta per $1 change in underlying
theta0.0000
Change in option price per 1 day decrease in time to expiry
vega0.0000
Change in option price per 1% increase in volatility
rho0.0000
Change in option price per 1% increase in interest rate
Greeks
delta0.0000
Change in option price per $1 change in underlying
gamma0.0000
Rate of change in delta per $1 change in underlying
theta0.0000
Change in option price per 1 day decrease in time to expiry
vega0.0000
Change in option price per 1% increase in volatility
rho0.0000
Change in option price per 1% increase in interest rate
Sensitivity to Spot Price
Sensitivity to Time to Expiry
Sensitivity to Volatility
Sensitivity to Interest Rate
Educational Notes
This calculator implements two option pricing models:
- Black-Scholes model for European options (closed-form solution)
- Binomial Tree model for American options (numerical method)
Key differences between European and American options:
- European options can only be exercised at expiration
- American options can be exercised at any time before expiration
- American options are more valuable due to the early exercise premium
- Dividend payments affect American options more significantly
Understanding the Greeks:
- Delta (Δ): Rate of change in option price with respect to underlying price
- Gamma (Γ): Rate of change in delta with respect to underlying price
- Theta (Θ): Rate of change in option price with respect to time
- Vega (V): Rate of change in option price with respect to volatility
- Rho (ρ): Rate of change in option price with respect to risk-free rate
Disclaimer: This calculator is for educational purposes only. Always consult with financial professionals for investment decisions.