Option Pricing Calculator
Price European call and put options using the Black-Scholes model.
Why Option Pricing Matters
Option pricing is essential for traders, investors, and risk managers to determine the fair value of call and put options. Mispricing creates arbitrage opportunities, while accurate valuation supports hedging and speculation.
How to Use This Calculator
Enter the current stock price, strike price, time to expiry, risk-free rate, and volatility. The calculator uses the Black-Scholes model to compute:
- Call & Put Prices
- Greeks: Delta, Gamma, Vega (risk sensitivities)
The Black-Scholes Formula
C = S·N(d₁) − K·e⁻ʳᵀ·N(d₂)P = K·e⁻ʳᵀ·N(−d₂) − S·N(−d₁)Where:
d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)d₂ = d₁ − σ√T- S = Spot price
- K = Strike price
- r = Risk-free rate
- T = Time to expiry (years)
- σ = Volatility
- N() = Standard normal CDF
Key Greeks
- Delta: Option price change per $1 move in stock
- Gamma: Rate of change of delta
- Vega: Sensitivity to volatility changes
Real-World Applications
- Trading: Identify under/overvalued options
- Hedging: Use delta to hedge portfolio risk
- Risk Management: Monitor gamma and vega exposure
- Employee Stock Options: Estimate fair value
Assumptions
- No dividends
- No transaction costs
- Constant volatility and interest rates
- Log-normal price distribution
- European-style (no early exercise)
Limitations
- Does not price American options (early exercise)
- Volatility is assumed constant (not realistic)
- Ignores market frictions like bid-ask spreads
- Assumes continuous trading and no jumps
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