Black-Scholes Option Pricer
Price European call and put options using the Black-Scholes model. Computes Greeks (delta, gamma, theta, vega, rho) and verifies put-call parity.
How It Works
Enter the spot (current) stock price and the strike price of the option. Set the days remaining until expiration. Input the implied volatility as a percentage (e.g., 20 for 20% annualized). Set the risk-free rate (commonly the Treasury bill yield matching the option's term). The calculator instantly prices both the call and put, computes all five Greeks, and verifies put-call parity.
Greeks are reported per-share (multiply by 100 for one contract). Theta is daily time decay. Vega and Rho are expressed as dollar changes per 1% move in volatility or rates: divide by 100 for a 1 basis point change. Use the Greeks to understand risk exposure, hedge ratios, and how market conditions affect your position.
FAQ
What is the Black-Scholes formula and how does it work?
The Black-Scholes formula prices European-style options using six inputs: current stock price, strike price, time to expiration, volatility, risk-free interest rate, and (implicitly) no dividends. It assumes log-normal stock returns and continuous trading. The output is a theoretical fair price for both call and put options.
What do the Greeks (delta, gamma, theta, vega, rho) tell me?
Delta measures how much the option price changes for a $1 move in the underlying. ATM calls have delta ~0.5. Gamma measures how fast delta changes: highest near the money. Theta is daily time decay: always negative for long options. Vega is sensitivity to a 1% change in implied volatility. Rho is sensitivity to a 1% change in interest rates.
What is put-call parity and why does it matter?
Put-call parity is a no-arbitrage relationship: Call + K*e^(-rT) = Put + Spot. If this equation doesn't hold, an arbitrage opportunity exists. Our calculator verifies put-call parity automatically: the difference should be near zero.
Does the Black-Scholes model work for American-style options?
American options can be exercised early. Black-Scholes assumes European exercise (only at expiration). For non-dividend stocks, American calls are worth the same as European calls. For American puts and dividend-paying stocks, Black-Scholes may undervalue the option.
How do I find the implied volatility for an option?
Implied volatility is the market's forecast of future volatility, derived by reverse-engineering the Black-Scholes formula from current option prices. Our calculator uses volatility as an input, so try different values: higher IV means higher option prices. Use IV from broker quotes or online sources.
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