Options Pricing Calculator
Black-Scholes option pricing model for European call and put options
Option Parameters
Examples: 0.25 = 3 months, 0.5 = 6 months, 1 = 1 year
Use Treasury rate matching option expiration
Annual standard deviation of returns. Higher = more expensive options
Moneyness
Option Values
Enter option parameters and click Calculate
Black-Scholes prices will appear here
Black-Scholes Model
Model Overview
The Black-Scholes model is the standard method for pricing European options. It assumes:
- European-style exercise (only at expiration)
- No dividends paid during option life
- Markets are efficient (no arbitrage)
- Returns are log-normally distributed
- Constant volatility and risk-free rate
Key Components
Intrinsic Value: Immediate exercise value. Call = max(S-K, 0), Put = max(K-S, 0).
Time Value: Additional value from possibility of favorable price movement before expiration.
Volatility (σ): Most critical input. Historical volatility uses past prices; implied volatility is derived from market option prices.
Greeks (Sensitivities)
Delta: Price change per $1 stock move. Call: 0-1, Put: -1-0.
Gamma: Rate of delta change.
Theta: Time decay per day.
Vega: Price change per 1% volatility change.
Rho: Price change per 1% rate change.
Practical Usage
Use this calculator to:
- Estimate fair value of options
- Compare to market prices for opportunities
- Understand impact of volatility changes
- Model different scenarios before trading
- Educational understanding of option pricing